"Find the derivatives of x=sin⁡h2y" was answered by our community

alesterp

Answered question

2021-10-13

Find the derivatives of

x = {\sin h}^{2} y

Answer & Explanation

BleabyinfibiaG

Skilled2021-10-14Added 118 answers

Step 1 Given

x = {\sin h}^{2} y

Step 2 Differentiating wrt x

\sin h = \sqrt{x}

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

Differentiating w.r.t x

\frac{d y}{d x} = \frac{1}{\sqrt{1 + {(\sqrt{x})}^{2}}} \cdot \frac{d}{d x} (\sqrt{x})

= \frac{1}{\sqrt{1 + x}} \frac{1}{2 \sqrt{x}}

= \frac{1}{2 \sqrt{x + x^{2}}}

∴ \frac{d y}{d x} = \frac{1}{2 \sqrt{x + x^{2}}}

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