finding the derivitive of f(x) = ln(x^4)

[tinad]

Find the derivitive of f(x) = ln(x^4)

Would the natural log stay the same and you find the derivitive of the (x^4)? Or is it as simple as 1/x^4 ?

 

[skeeter]

using the laws of logarithms ... ln(x⁴) = 4ln(x)

the derivative would be 4/x.

 

[Euler]

Or you could do it the long way, using the chain rule:

\(\displaystyle \L\,ln(x^4)=\frac{1}{x^4}*\frac{4x^3}{1}=\frac{4}{x}\)