Question

How do you find `dy/dx` given `x=2y^5+y^3+4`?

Answer 1

Use implicit differentiation.

Explanation:

Given `x = 2y^5 + y^3 + 4`

Differentiate each term:

`(d(x))/dx = (d(2y^5))/dx + (d(y^3))/dx + (d(4))/dx`

`1 = 10y^4dy/dx + 3y^2dy/dx`

`(10y^4 + 3y^2)dy/dx = 1`

`dy/dx = 1/(10y^4 + 3y^2)`