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Home Q & A Board Science-Related Homework Help Mathematics Calculus
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Orlando0 Orlando0
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3 years ago
3. z(t)=√3t - 4 please help
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#1
Educator
3 years ago
Notice there are two terms here. The second term is a constant, so its derivative it zero. Therefore, we're left with only a single term being \(f\left(x\right)=\sqrt{3x}\). Luckily, we have a video on the \(y=\sqrt{x}\), so the solution is practically the same.

The final answer you should get is:

\(f'\left(x\right)=\frac{3}{2\sqrt{3x}}\)

In the video for \(y=\sqrt{x}\), the answer is \(f'\left(x\right)=\frac{1}{2\sqrt{3x}}\)

Hope it helps!
Orlando0 Author
wrote...
#2
3 years ago
thx u, but this is using the delta method and I want to know how this will be solved with first principles
wrote...
#3
Educator
3 years ago
Quote from: Orlando0 (3 years ago)
thx u, but this is using the delta method and I want to know how this will be solved with first principles

Oh, first principles is the same as delta method. In the "delta method" you use \(\lim _{\Delta x\to 0}\), while in the "first principles" you use \(\lim _{h\to 0}\). Literally the same, just change all \(\Delta x\)'s to \(h\)'s
Orlando0 Author
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#4
3 years ago
This is what I did so far but i think its wrong so far. mind taking a look?
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#5
Educator
3 years ago
Made a mistake early on, right at the beginning.

sqrt(3x)

inserting (x+h) gives you:

sqrt(3(x+h))
= sqrt(3x+3h)

You wrote: sqrt(3x+h)... make that correction and start over...
Orlando0 Author
wrote...
#6
3 years ago
is 3(t + h) the answer when multiplying √3(t + h) and √3(t + h) ?
wrote...
#7
Educator
3 years ago
Quote from: Orlando0 (3 years ago)
is 3(t + h) the answer when multiplying √3(t + h) and √3(t + h) ?
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