हिंदी

If then findy=(sinx)x+sin-1x then find dydx

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प्रश्न

If `y=(sinx)^x + sin^-1 sqrtx  "then find"  dy/dx` 

योग
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उत्तर

\[\text{ We have, y }= \left( \sin x \right)^x + \sin^{- 1} \sqrt{x}\]

y = u + v

`dy/dx = (du)/dx + (dv)/dx`

`u = (sin x)^x, v = sin^-1 sqrtx`

log u = x log sin x

`1/u (du)/dx = log(sin x) + x 1/sin x cot x`

`du/dx = (sin x)^x [log sin x + x cot x]`

`(dv)/dx = 1/sqrt(1-x) xx 1/(2sqrtx)`

`dy/dx = (sin x)^x [log sin x + x cot x] + 1/(2sqrtx sqrt1-x)`

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अध्याय 10: Differentiation - Exercise 11.05 [पृष्ठ ८९]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 10 Differentiation
Exercise 11.05 | Q 28 | पृष्ठ ८९
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