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Differentiation Using Substitution

Differentiate...

Question

Differentiate the expressions with respect to $x$
$x^{2} sin h^{- 1} (2 x)$

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Solution

$\frac{d}{d x} s i n h^{- 1} x = \frac{1}{\sqrt{x^{2} + 1}}$

$\Rightarrow \frac{d}{d x} (x^{2} s i n h^{- 1} 2 x) = 2 x \times s i n h^{- 1} (2 x) + x^{2} \times \frac{2}{\sqrt{4 x^{2} + 1}}$

$\Rightarrow \frac{d}{d x} (x^{2} s i n h^{- 1} 2 x) = 2 x (s i n h^{- 1} (2 x) + \frac{x}{\sqrt{4 x^{2} + 1}})$

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