Differentiate lnx/x^5
Using the quotient rule I got a final answer of x^4-lnx5x^4/x^10
First of all is this correct, if so is it in its simplest form.
Please help, thanks.
recall that by the product rule we have that $\displaystyle \frac d{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)$
here we have $\displaystyle f(x) = \left( x^4 + 3 \right)^3 \implies f'(x) = 12x^3 \left( x^4 + 3 \right)^2$ by the chain rule
and $\displaystyle g(x) = \cos 2x \implies g'(x) = -2 \sin 2x$ also by the chain rule
now just put the pieces together. with practice you will be able to do all this in one line without splitting up the parts like this, so keep at it