Best solutions to - "Find the derivatives of the following functions. f(v)=sin⁡h−1v2" - Plainmath

Isa Trevino

Answered question

2021-05-04

Find the derivatives of the following functions.

f (v) = {\sin h}^{- 1} v^{2}

Answer & Explanation

Lacey-May Snyder

Skilled2021-05-06Added 88 answers

Step 1
Consider the given function,

f (v) = {\sin h}^{- 1} (v^{2})

use the chain rule to find the derivative of the above function,

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

use the formula,

\frac{d}{d x} {\sin h}^{- 1} (x) = \frac{1}{\sqrt{x^{2} + 1}}

Step 2
so, the derivative of the given function will be,

\frac{d}{d v} [{\sin h}^{- 1} (v^{2})] = \frac{1}{\sqrt{{(v^{2})}^{2} + 1}} \cdot \frac{d}{d v} (v^{2})

= \frac{1}{\sqrt{{(v^{2})}^{2} + 1}} \cdot (2 v)

= \frac{2 v}{\sqrt{v^{4} + 1}}

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