If y-esin2x-sin4x-sin6x- then dydx-

y=e^sin^2x+sin^4x+....∞ sin^2x+sin^4x+...∞=a1 r=sin^2x1 sin^2x sin^2xcos^2x=tan^2x y=e^tan^2x log y=tan^2x 1ydydx=2tan x sec^2x ...

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Basic Differentiation Rule

If y=esin2x...

Question

If $y = e^{{sin}^{2} x + {sin}^{4} x + {sin}^{6} x + . . . . . \infty}$ , then $\frac{d y}{d x} = ?$

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y = e^{{sin}^{2} x + {sin}^{4} x + {sin}^{6} x + . . . . \infty}

\frac{d y}{d x} =

y = e^{{{sin}^{2} x + {sin}^{4} x + {sin}^{6} x + \dots}}

\frac{d y}{d x} =

$If~y=exp {s i n^{2} x + s i n^{4} x + s i n^{6} x + . . . . . . .} t h e n \frac{d y}{d x} =$

y = e^{{({sin}^{2} x + {sin}^{4} x + {sin}^{6} x + \dots) {log}_{e} 2}}

x^{2} - 17 x + 16 = 0,

0 < x < \frac{π}{2} .

List I

List II .

\begin{matrix} List I & List II (a) & \frac{2 sin 2 x}{1 + {cos}^{2} x} & (p) & 1 (b) & \frac{2 sin x}{sin x + cos x} & (q) & \frac{4}{9} (c) & \infty \sum n = 1 (cot x)^{n} & (r) & \frac{2}{3} (d) & \infty \sum n = 1 n (cot x)^{2 n} & (s) & \frac{4}{3} \end{matrix}

e^{({sin}^{2} x + {sin}^{4} x + {sin}^{6} x + . . . \infty) {log}_{e} 2}

x^{2} + 7 x + 16 = 0

\frac{2 cos x}{sin x + 2 cos x} (0 < x < \frac{π}{2})

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