Question

What is the derivative of `y = ((x^2 + 5) / (x^2 - 5))^5`?

Answer 1

`dy/dx= (-100x(x^2 + 5)^4)/(x^2 - 5)^6`

Explanation:

Use the chain rule.

Let `y = u^5` and `u = (x^2 + 5)/(x^2 -5)`.

`dy/dx= 5u^4 * (2x(x^2 - 5) - (2x(x^2 + 5)))/(x^2 - 5)^2`

`dy/dx = 5u^4 * (2x^3 - 10x - 2x^3 - 10x)/(x^2 -5)^2`

`dy/dx = 5u^4 * (-20x)/(x^2 -5)^2`

`dy/dx= (-100x((x^2 + 5)/(x^2 -5))^4)/(x^2 -5)^2`

`dy/dx= (-100x(x^2 + 5)^4)/(x^2 - 5)^6`

Hopefully this helps!