Find the second order derivatives of the following functions: ( ) - Vidyadip

Question

Find the second order derivatives of the following functions:$\log(\sin\text{x})$

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Answer

We have,
$\text{y}=\log(\sin\text{x})$
Differentiating w.r.t.x, we get
$\frac{\text{dy}}{\text{dx}}=\frac{1}{\sin\text{x}}\times\cos\text{x}=\cot\text{x}$
Differentiating w.r.t.x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\text{cosec}^2\text{x}$

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