Question

Differentiate the function.
y = ln(x^9 sin^2 x)

Answer 1

Recall:\[\Large \left[\ln(stuff)\right]' \quad=\quad \frac{1}{stuff}(stuff)'\]

Answer 2

\[\Large y'\quad=\quad \frac{1}{x^9 \sin^2 x}\left(x^9 \sin^2 x\right)'\]

Answer 3

So we have to take the derivative of that second part there.
Product rule will help us out nicely.\[\Large y'\quad=\quad \frac{1}{x^9 \sin^2 x}\left[\color{royalblue}{(x^9)'}\sin^2 x+x^9\color{royalblue}{(\sin^2x)'}\right]\]

Answer 4

Then just take the derivative of the blue parts, and boom yer done!

Answer 5

thank you so much!!

Answer 6

Wasn't this already answered?