Question

Take the derivative of sin^2[lnx]

Answer 1

\[f(x)=\sin^2(\ln(x))\] like that?

Answer 2

or
\[f(x)=\sin^2(x)\ln(x)\]

Answer 3

first one requires the chain rule twice
second one the chain and produce rule

Answer 4

the first one

Answer 5

ok first visualize it as
\[\huge \left(\sin(\ln(x))\right)^2\]

Answer 6

since that is what the square means on the sine
then work from the outside in using the chain rule
the derivative of something squared is two times something, times the derivative of the something

Answer 7

the derivative of the sine of something is the cosine of something times the derivative of something

Answer 8

and the derivative of the log is \(\frac{1}{x}\)

Answer 9

I got this:
2(sin[lnx])(cos[lnx})(1/x)

Answer 10

looks good to me

Answer 11

Can I simplify that even more? @satellite73

Answer 12

there is no such mathematical operation as "simplify" but no you cannot do anything with it unless you want to rewrite is as
\[\frac{2\sin(\ln(x))\cos(\ln(x))}{x}\]

Answer 13

oh okay. Thanks for your help! :)

Answer 14

yw