Implicit differentiation? Please show me how you did the work thanks alot?

Question

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

(p + 1)q^2 = 10000

Answer 1

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.

Answer 2

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 3

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.

Answer 4

Let's do this properly, with implicit differentiation.



(p+1)q^2 = 1000



pq^2 + q^2 = 1000



Differentiate both sides...

q^2 + 2pq(dp/dq)+2q(dp/dq) = 0



2p(dp/dq)+2(dp/dq) = -q



2(dp/dq)(p+1) = -q



(dp/dq) = -q/(2p+2)