if-y-sinx-e-x-find-d-e-sin-1-y-d-lnx-

Question Number 166585 by mkam last updated on 22/Feb/22

i f y = {(s i n x)}^{e^{x}} f i n d \frac{d (e^{{s i n}^{- 1} y})}{d (l n x)}

Answered by Eric002 last updated on 22/Feb/22

l n (y) = e^{x} l n (s i n (x))

\frac{d y}{d x} = e^{x} {(s i n (x))}^{e^{x}}) (c o t (x) + l n (s i n (x))

d (e^{{s i n}^{- 1} (y)}) / d (l n (x)) = \frac{x e^{{s i n}^{- 1} (y)} / \sqrt{1 - y^{2}}}{d x} d y

= e^{x} {(s i n (x))}^{e^{x}} (c o t (x) + l n (s i n (x))) (\frac{{x e}^{{s i n}^{1} (y)}}{\sqrt{1 - y^{2}}})

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