Calculus home work

Question

Find dy/dx in terms of x and y if ax3 – by5= c3 . Assume that a, b and c are constants.

dy/dx =

Answer 1

This is an implicit derivation problem.

ax³ - by⁵ = c³

Taking the implicit derivative of both sides of the equation:

3ax² - 5by⁴dy/dx = 0

Solve for dy/dx

5by⁴dy/dx = 3ax²

dy/dx = 3ax²/(5by⁴)