finding the derivative

Question

y=ln(5x^2)

Answer 1

There's an easy way to do this. The log of anything squared is 2 times the log.
y=ln(5x^2)=ln(5)+2ln(x) and the derivative dy/dx=2/x.
Another approach is set z=5x^2 so dz/dx=10x and y=ln(z) making dy/dz=1/z.
dy/dx=dy/dz*dz/dx=1/z*10x=1/(5x^2)*10x=10x/(5x^2)=2/x.