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dasmartypants3 dasmartypants3
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12 years ago
Can you show me how to get the derivative of this functin by using implicit differentiation? Thanks Alot

(p + 1)q^2 = 10000
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wrote...
#1
12 years ago
You have not said what the derivitive is with respect to. Are we differentiating with respect to time (t) or distance (x)? If you want help you need to specify the problem precisely.
wrote...
#2
12 years ago
I'm going to change to x & y.

(x+1)(y^2)=1000  differentiate both sides in terms of x.  use product rule.

(x+1)(2y)(dy/dx) + (y^2)(1)=0  isolate dy/dx

(x+1)(2y)(dy/dx) = -(y^2)

(dy/dx) = -(y^2)/[(x+1)(2y)]

If you are differenciating with respect to x, differentiat x terms as usual, but everytime you differenciate the y term, stick on a dy/dx.

Hope this helps.
wrote...
#3
12 years ago
i dont know what u mean by implicit but i can differentiate it

first isolate one variable i'll isolate p

(p+1)(q^2) = 10000
p+1 = 10000 / q^2
p = 10000/(q^ 2)  - 1

dq/dp = [(q^2)(0) - (10000)(2q)(1)] / [(q^2)^2]  - 0  
= ( -20000q ) / q^4
= -20000 / q ^ 3      
Answer accepted by topic starter
michellllemackmichellllemack
wrote...
#4
12 years ago
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