y -sin -1 frac1 sqrt x-1 Find dy - dx

Let y=sin^ 11/√(x+1) dy/dx=d/dx(sin^ 11/√(x+1)) =1/√(1 (1/√(x+1) )^2).d/dx(1/(x+1)^1/2) [ ∵d/dx(sin^ 1x)=1/√(1 x^2) ] =1/√(x+1 1/x+1).d/dx.(x+1)^ 1/2 = ...

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Byju's Answer

Standard XII

Mathematics

Variable Separable Method

y =sin ∧-1 fr...

Question

$y = s i n^{- 1} \frac{1}{\sqrt{x + 1}}$

Find $\frac{d y}{d x}$

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Solution

Let $y = s i n^{- 1} \frac{1}{\sqrt{x + 1}} \frac{d y}{d x} = \frac{d}{d x} (s i n^{- 1} \frac{1}{\sqrt{x + 1}}) = \frac{1}{\sqrt{1 - {(\frac{1}{\sqrt{x + 1}})}^{2}}} . \frac{d}{d x} (\frac{1}{(x + 1)^{\frac{1}{2}}}) [∵ \frac{d}{d x} (s i n^{- 1} x) = \frac{1}{\sqrt{1 - x^{2}}}] = \frac{1}{\sqrt{\frac{x + 1 - 1}{x + 1}}} . \frac{d}{d x} . (x + 1)^{\frac{- 1}{2}} = \sqrt{\frac{x + 1}{x}} . \frac{- 1}{2} (x + 1)^{- \frac{1}{2} - 1} . \frac{d}{d x} (x + 1) = \frac{(x + 1)^{\frac{1}{2}}}{x^{\frac{1}{2}}} . - \frac{1}{2} (x + 1)^{\frac{- 3}{2}} = \frac{- 1}{2 \sqrt{x}} . (\frac{1}{x + 1})$

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y=sin−11√x+1 Find dydx

Let y=sin−11√x+1dydx=ddx(sin−11√x+1)=1√1−(1√x+1)2.ddx(1(x+1)12) [∵ddx(sin−1x)=1√1−x2]=1√x+1−1x+1.ddx.(x+1)−12=√x+1x.−12(x+1)−12−1.ddx(x+1)=(x+1)12x12.−12(x+1)−32=−12√x.(1x+1)

$y = s i n^{- 1} \frac{1}{\sqrt{x + 1}}$

Find $\frac{d y}{d x}$