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प्रश्न
Derivative of `e^(sin^2x)` with respect to cos x is ______.
पर्याय
`sin x e^(sin^2x)`
`cos x e^(sin^2x)`
`−2 cos x e^(sin^2x)`
`−2 sin^2 x cos x e^(sin^2x)`
MCQ
रिकाम्या जागा भरा
उत्तर
Derivative of `e^(sin^2x)` with respect to cos x is `bbunderline(−2 cos x (e^(sin^2x)))`.
Explanation:
u = `e^(sin^2x) and v = cos x`
∴ `(du)/(dx) = e^(sin^2x) (2 sin x) cos x`
and `(dv)/(dx) = -sin x`
Thus, `(du)/(dv) = (du"/"dx)/(dv"/"dx)`
= `(e^(sin^2x).2sin x.cosx)/-sin x`
= `-2 cos x e^(sin^2x)`
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