Question

what is the derivative of f(x)=ln((x^(8)-8)^(5))

Answer 1

The derivative of the natural log function is
\[\frac{d}{dx}[\ln u(x)]=\frac{u'(x)}{u(x)}\]
In this case, \(u(x)=\left(x^8-8\right)^5\). However, you can use a log property to rewrite the function:
\[f(x)=\ln\left(x^8-8\right)^5\\
f(x)=5\ln\left(x^8-8\right)\]
So, you have
\[f'(x)=5\frac{\frac{d}{dx}[x^8-8]}{x^8-8}\]

Answer 2

thank you so much!!

Answer 3

You're welcome