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Differentiate {{}^{{2}}{x}}w.r.t {e}^{{{{{x}}}}}.

Question

Differentiate $sin^{2} x$ w.r.t $e^{c o s x}$ .

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Michael Discussed

Differentiate

sin^{2} x

w.r.t

e^{c o s x}

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Text solutionVerified

Solution: We know that

\frac{d y}{d z}

can be written as

\frac{d y}{d z} = \frac{\frac{d y}{d x}}{\frac{d z}{d x}}

.
So, here,

y = sin^{2} x

and

z = e^{c o s x}

∴ \frac{d y}{d x} = 2 sin x cos x

\frac{d z}{d x} = - sin x (e^{c o s x})

∴ \frac{d y}{d z} = \frac{\frac{d y}{d x}}{\frac{d z}{d x}} = \frac{2 sin x cos x}{- sin x ( e ^{c o s x} )} = \frac{- 2 cos x}{e ^{c o s x}}

∴ \frac{d y}{d z} = \frac{- 2 cos x}{e ^{c o s x}}

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Question Text	Differentiate $sin^{2} x$ w.r.t $e^{c o s x}$ .
Answer Type	Text solution:1
Upvotes	150