We have an answer to "If y(x)=arcsin⁡u, then y" - Plainmath

facas9

Answered question

2021-09-28

If

y (x) = \arcsin u

, then y

Answer & Explanation

aprovard

Skilled2021-09-29Added 94 answers

Step 1
If y(x)=f(u)
By chain Rule of derivative

\frac{d y}{d x} = \frac{d}{d u} (f (u)) \cdot \frac{d u}{d x}

= f^{'} (u) \cdot \frac{d u}{d x}

Step 2
Here

y (x) = \sin^{- 1} u

\Rightarrow y^{'} = \frac{d}{d u} (\sin^{- 1} u) \cdot \frac{d u}{d x}

= \frac{1}{\sqrt{1 - u^{2}}} \cdot \frac{d u}{d x}

= \frac{u^{'}}{\sqrt{1 - u^{2}}}

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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