What is the derivative of ${sin}^{2} (ln x)$ $sin^2(lnx)$ ?

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Answer 1 · 2015-04-03T16:35:31

$f (x) = {sin}^{2} (ln x) = {(sin (ln x))}^{2}$ $f(x)=sin^2(lnx) = (sin(lnx))^2$

To find $f'(x)$ , use the chain rule, twice.

$f'(x)=2(sin(lnx))*[cos(lnx)*1/x]$

(The factor in the brackets is the derivative of $sin(lnx)$ )

Clean up the answer however you want.

$f'(x)=2/ x sin(lnx)cos(lnx) 1/x sin(2lnx) = 1/x sin(lnx^2)$

What is the derivative of sin^2(lnx)sin2(lnx)sin^2(lnx)?