Question

y = (cos 3x)^x Use logarithmic differentiation to find the derivative of the function.

Answer 1

take the log, get
\[x\ln(\cos(3x)\] then find the derivative using the product rule and the chain rule, then mult)iply your result by \[(\cos(3x))^x\]

Answer 2

\[(fg)'-f'g+g'f\] with
\[f(x)=x,f'(x)=1,g(x)=\ln(\cos(3x)),g'(x)=\frac{-3\sin(3x)}{\cos(3x)}\]

Answer 3

i suppose you could write \(g'(x)=-3\tan(3x)\) if you want to look sharp