What is the derivative of this logarithmic and exponential function?: x^2 ln(x^5)

Question

I know to set it up like (x^2)[ln(x^5)]' + (x^2)'[ln(x^5)] but am confused how to proceed from this. In-depth steps would be appreciated.

Answer 1

You can make it easier by using the log rule for exponents: 5 x²lnx

The derivative of x² and lnx should be easy to obtain.

note that d/dx of ln(x⁵) = (1/x⁵)5x⁴ = 5/x which is the derivative of 5ln(x)