Question

If x^3+y^2=31, find the value of dy/dx at the point (3,2)

Answer 1

First, solve the equation for y. Then differentiate it with respect to x to find dy/dx, and plug in your known point.

Answer 2

so y=(-x^3+31)^(1/2)

Answer 3

derivative of that is -(3x^2)/(2sqrt(31-x^3))

Answer 4

So -9/8

Answer 5

-9/4 I mean

Answer 6

Argh, I mean -27/4

Answer 7

There we go! :-)

Answer 8

Sorry, doing it in my head. Cool. Thanks,

Answer 9

You could also take the derivative of the whole equation with respect to x (using the chain rule) and after some algebra get dy/dx = -3x2/2y

Answer 10

Sounds good. :)

Answer 11

Left as an exercise for the reader, as they say in the textbook biz :-)