Question

f(x)=ln(ex^3/((x-6)^6)) find derivative. And then find d/dx(e^f(x))

Answer 1

Use the properties of logarithms to simplify the function.

Answer 2

\[f'(x)=-\frac{3(x+6)}{x(x-6)}\]

Answer 3

\[e^{f(x)}=ex^3/(x-6)^6\]\[e'(x)=-3ex^2\frac{(x+6)}{(x-6)^7}\]