How would I find a derivative with ln in the exponent?

Question

H (z)=z^ln6  + ln5

I know how to take the derivative of the second part using the ln rule. I would get 1/5, but I don't know how to do it for the first part of the function since the ln is in the exponent. 

Answer 1

H(z) = z^ln6 + ln5

 

Note the ln6 in the exponent is a constant, so the first term is of the form z^k.  Just use the exponent rule on this one.  The second term is a constant, so its derivative is zero.

 

dH/dz = (ln6)z^ln6-1