What is the derivative of $y=(sinx)^(2x)$ ?

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Answer 1 · 2017-03-02T12:14:14

$dy/dx = 2sin^(2x)(x)(x cotx + ln(sinx))$

$y = (sinx)^(2x) = sin^(2x)(x)$

$lny =2x*ln(sinx)$

Applying Implicit differentiation, the product rule, standard differentials and the chain rule:

$1/y dy/dx = 2x*1/sinx * cosx + ln(sinx)*2$

$dy/dx = y*(2x*cosx/sinx +2ln(sinx))$

$= y* 2(xcotx+ln(sinx))$

$= (sinx)^(2x)*2(xcotx+ln(sinx))$

$= 2sin^(2x)(x)(x cotx + ln(sinx))$

What is the derivative of y=(sinx)^(2x)y=(sinx)^(2x)?