How to find the derivative of natural logarithm

Question

How would I go about differentiating this function:

f(x)=[ln(x^5-4)]^3

Would I use the power rule and chain rule?

Answer 1

Hello Dwayn,

You would use both the power rule and chain rule. The way I'm doing it below is not the only way, but one I'm most familiar with.

if you set u = ln(x⁵ - 4), then u' = (derivative of x⁵ -4) / (x⁵ -4) = 5x⁴/(x⁵ -4)

The original function is f(x)=[ln(x^5-4)]^3 which you could rewrite as u³

To find derivative of u³, we would use the power rule: (u³)' = 3 * u' * u²

So: (u³)' = 3 * 5x⁴/(x⁵ -4) * [ln(x⁵ -4)]^2 = 15 * x⁴ * [ln(x⁵ -4)]² / (x⁵ -4)