Calculus

Derivative of transcedental function

Derivative of transcedental function

find y'' if y=cos3xsin2x,   and if x=60°
         y'=cos3x•d/dx(sin2x)+sin2x•d/dx(cos3x)
         y'=cos3x•cos2x•2+sin2x(-sin3x)•3
&nbs

Deckz   52   1 Reply

duddy

Finding the derivative of the given function

Finding the derivative of the given function

f(t)=[2/squareroot(t)]+[6/cuberoot(t)]

The answer my book was :
(-t^1/2+2t^2/3)/t^2


Yet i'm getting different answer, can someone try it ? Hoping we got same answer  

Deckz   82   4 Replies

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Deckz

How to plot the graph of product of trignomatric and exponential function of base e without table

How to plot the graph of product of trignomatric and exponential function of base e without table

 plot e^x cosx without point table

tamim   20   1 Reply

bio_man

Integrate dy/square root of y+4 minus 2

Integrate dy/square root of y+4 minus 2

Integrate dy/square root of y+4 minus 2

Allen z   28   1 Reply

bio_man

Calculus differential equation (not sure which type)

Calculus differential equation (not sure which type)

A population r(t) of rabbits (at time t) satisfies
dr/dt = kr (1 − (r/r∗)) − αfr                                       (1)
where k > 0 i

yungdumb   72   5 Replies

duddy

The population of a

The population of a

1.The population of a certain state (in thousands) at t years since 1991 is modeled by the polynomial p(t)=-0.24t^2+111t+6766.

a. Find the average growth rate from 1991 to 2001 analytically.
b. Find the instantaneous growth rate in 19

yoyoyo12345   26   3 Replies

bio_man

12.Determine analytically, showing all work, all values of x (if any) at which the the func on f(x)

12.Determine analytically, showing all work, all values of x (if any) at which the the func on f(x)

1. Find analytically the equation of the line that is tangent to g(x)=sqrt（-x-3 ）and parallel to the line y=-1/2x+2. Use the limit definition of the derivative and find the point of tangency by hand, showing all work. Verify your results by sketching

ccnnieeee   40   1 Reply

bio_man

What is the integral of √(a-y) /√y

What is the integral of √(a-y) /√y

What is the integral of √(a-y) /√y

Rentz   27   1 Reply

bio_man

Determine whether or not of the following statements are true or false, and give explanations or cou

Determine whether or not of the following statements are true or false, and give explanations or cou

1. Determine whether or not of the following statements are true or false, and
give explanations or counterexamples for each.

If a < b and f ( a ) < L < f ( b ), then there is some value of c in ( a , b ) for which f ( c ) =

chansamhua   70   11 Replies

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bio_man

If f(x) = g(x) for all values of x except possibly for x = 2 and limx→2 g(x)=5 , then

If f(x) = g(x) for all values of x except possibly for x = 2 and limx→2 g(x)=5 , then

1. If f(x) = g(x) for all values of x except possibly for x = 2 and limx→2 g(x)=5 , then
a. f(2)=5
b.limx→2 f(x)may not equal 5
c.limx→2f(x)=5

2.If f(x)={4x+1 if xnot equals to , x+b if x=0} and limx→0 f(x)=f(0) , then

ccnnieeee   76   5 Replies

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bio_man

For the position function s(t) = −16t^2+110t : a) Complete the following table with the ...

For the position function s(t) = −16t^2+110t : a) Complete the following table with the ...

For the position function s(t) = −16t^2+110t :

a) Complete the following table with the appropriate average velocities (show work and
give up to 3 decimal places)
Time Interval    [0.99, 1]        &n

ccnnieeee   42   3 Replies

duddy

Use a reference triangle to find the exact value of cos[arctan(-3/10)]

Use a reference triangle to find the exact value of cos[arctan(-3/10)]

1. Use a reference triangle to find the exact value of cos[arctan(-3/10)]
2.y= arctan(1/x),  Use a reference triangle to find cos y.

ccnnieeee   33   3 Replies

duddy

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .
What is the average velocity over the interval [0, 2] ?
2. The position of an object moving along a line is s(t) = t^2-2t . Approximate the instantane

ccnnieeee   40   4 Replies

bio_man

Find the derivative of the inverse trig fn below

Find the derivative of the inverse trig fn below

I literally don't know how to solve it because every time i'am getting a wrong answer so I need help Guys

b=arcsec[(a^2+1)/(a^2-1)]

Inverse trig fn   49   1 Reply

bio_man

Delta method versus quotient rule

Delta method versus quotient rule

\(f\left(x\right)=\frac{3}{x^2+1}\)

Applying the quotient rule, notice how the denominator is now squared:

[math=inline]f'\left(x\right)=\frac{\left(0\right)\left(x^2+1\right)-\left(3\right)\left(2x\right)}{

bio_man   98   N/A

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bio_man

Solving for d^2/dx^2

Solving for d^2/dx^2

Need help checking my paper if I did the right process or not
I've attached it

Deckz   105   5 Replies

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bio_man

Use the Delta Method to derive the variance for the quantity [E(Xt^2 )]^3.

Use the Delta Method to derive the variance for the quantity [E(Xt^2 )]^3.

This is a question on my Asset Pricing assignment. I don't know how to calculate this one by delta method.

Wendy   81   1 Reply

bio_man

Find the required derivatives using appropriate formula

Find the required derivatives using appropriate formula

#1. Start w

bio_man   80   1 Reply

Kevin666

How to get the Y' of this function ?

How to get the Y' of this function ?

I really dont know how did the answer turned down to y/x based from my textbook 
Can you show me how it was done ?

Deckz   96   1 Reply

bio_man

How to solve for the derivative of this trig. function ?

How to solve for the derivative of this trig. function ?

see the atrached img. 

Deckz   63   3 Replies

bio_man

Finding the derivative of inverse tangent

Finding the derivative of inverse tangent

From the image, your function is: [mat

bio_man   164   N/A

bio_man

Find the derivative of

Find the derivative of

[math=inline]x\cdot \sin y

bio_man   191   N/A

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bio_man

Delta method question!

Delta method question!

Find the derivative of this by the delta method

\(y=x^2+3x-\frac{2}{x}\)

\(\frac{dy}{dx}=\lim _{\Delta x\rightarrow 0}\left(x^2+3x-\frac{2}{x}\right)\)

Apply [math=inl

bio_man   113   N/A

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bio_man

Chain rule help

Chain rule help

\(y=\sqrt{u^2-1}\)
\(u=4\sqrt{x}\)

Put u into x

\(y=\sqrt{\left(4\sqrt{x}\right)^2-1}\)

Simplify:

\(y=\sqrt{16x-1}\)

bio_man   202   N/A

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bio_man

Rules of differentiation Discussion

Rules of differentiation Discussion

These rules you have nothing to worry about. They're there to make differentiation easier to do, that's all.

Examples:

[highligh

bio_man   73   N/A

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bio_man

Delta method for x√x

Delta method for x√x

If you've been given:

\(x\cdot \sqrt{x}\)

You have to first change it into fractional exponents:

\(x\cdot x^{\frac{1}{2}}\)

Then use the exponent laws t

bio_man   106   1 Reply

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bio_man

Delta method calculus for ³√x²

Delta method calculus for ³√x²

Set:

\(f\left(x\right)=\sqrt[3]{x^2}\)

Apply into limit expression, do not take the limit yet:

[math=inline]\lim _{x\rightarrow 0}\ \frac{\sqrt[3]{\left(x+\Delta x\right)^2}-\sqrt[3]{x^2}

bio_man   134   N/A

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bio_man

Cube root of x by the Delta Method

Cube root of x by the Delta Method

\(f\left(x\right)=\sqrt[3]{x}\)

\(\lim _{x\rightarrow 0}\ \frac{\sqrt[3]{x+\Delta x}-\sqrt[3]{x}}{\Delta x}\)

Recall:

[math=inline]a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)

bio_man   99   1 Reply

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bio_man

Derivative by the delta method

Derivative by the delta method

Determine an equation of the line that is perpendicular to the tangent to the graph of f(x)=1/( x )  at x=2 and that intersects it at the point of tangency.

klcarrasquillo   63   1 Reply

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veronee_madison

Expand (x + Δx)²

Expand (x + Δx)²

Answer:

(x + Δx)² = (x + Δx)(x + Δx)

We 'expand' (aka FOIL) by multiplying each term:

x*x = x²
x*Δx = xΔx
Δx*x= xΔx
Δx*Δx = Δx²

[

bio_man   78   1 Reply

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gaminglifex

Applying Newton's law of cooling and differential equations

Applying Newton's law of cooling and differential equations

Suppose we place a 90 °C cup of coffee into a 20 °C room. If the coffee is in a Styrofoam cup for which k≈−0.05, what is the temperature of the coffee as a function of time?

chementhusiast   79   1 Reply

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austire

Differential equations with exponential growth and decay

Differential equations with exponential growth and decay

The rate of change of the amount of morphine in the human bloodstream is proportional to the amount of morphine present. If initially there is 0.4 mg of morphine in the bloodstream, and only 0.2 mg remains after 3 hours, find an equation for the amou

chementhusiast   48   1 Reply

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zar

Differential equations with exponential growth and decay

Differential equations with exponential growth and decay

Suppose that a rumour spreads according to dP/dt=1.1P. If 3 people know the rumour initially, how many people will know the rumour as a function of time?

chementhusiast   50   1 Reply

Bella_23

How to setup and solve differential equation problems

How to setup and solve differential equation problems

A certain small country has $10000 million in paper currency in circulation and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever ol

chementhusiast   62   1 Reply

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bio_man

How to setup and solve differential equation problems

How to setup and solve differential equation problems

A 15 000 ft^3  room has 20 ppm smoke. Fresh air enters at a rate of 1200 ft^3/min and forces the smoky air out. What is the smoke content as a function of time?

chementhusiast   42   1 Reply

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jayjayhussle310

How to setup and solve differential equation problems

How to setup and solve differential equation problems

A tank contains 10 L of water with 4 g/( L )  of dissolved salt. Water containing 2 g/( L )  of salt enters the tank at a rate of 7 L/( min ). The solution is kept thoroghly mixed and drains from the tank at the same rate.

How m

chementhusiast   43   1 Reply

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jamiebonf99

How do I setup and solve differential equation problems

How do I setup and solve differential equation problems

Suppose we have 7000 L of water with 50 kg of salt in it. If we add pure water at a rate Of 2 L/min and add water containing 0.6 kg/L of salt at a rate of 9 L/min, and we know that water flows out at a rate of 11 L/min, then what is the salt content

chementhusiast   64   1 Reply

potatobraiinz

Convert verbal statements into algebraic equations

Convert verbal statements into algebraic equations

If twice a certain number is increased by 9, the result is equal to 2 less than triple the number. Find the number.

After a certain number diminished by 8, the amount remaining is multiplied by 8; the result is the same as if the number we

Goalchi   44   1 Reply

duddy

Solve second-order differential equations when the right side is zero

Solve second-order differential equations when the right side is zero

My first question on Bioforums:

Solve the equation y^′′−3y^′+2y=0.

Solve the equation y^′′−5y′=0.

Goalchi   47   1 Reply

duddy

Solving 2nd order differential equations

Solving 2nd order differential equations

Solve the equation y^′′=x^2  (where x is in radians) if y^′=1 at the point (0, 0).

Please and thanks

chementhusiast   46   1 Reply

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duddy