Horacio L. answered • 10/25/19

High School and University Math/Physics Tutor

I'm going to keep the "out" part out so that

G=20log(10V)

We know that generally,

d/dx[log(x)]=1/xln(a)

but we must apply the chain rule, or the "derivative of the outside times the derivative of the inside" rule.

That is, we have multiply the derivative of log with the derivative of the stuff inside the parentheses, where

dG/dV=(20/V*ln(10))*(10)=30/V*ln(10)=(30/ln(10))*(V^-1)

I purposefully wrote it in an unaesthetic way, but now the second derivative is just a power rule question