Differentiate the following functions with respect to x: ( ^2) - Vidyadip

Question

Differentiate the following functions with respect to x:
$\log(\cos\text{x}^2)$

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Answer

Consider $\text{y}=\log(\cos\text{x}^2)$
Differentiate it with respect to x and applying the chain and product rule, we get
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\log(\cos\text{x}^2)$
$=\frac{-2\text{x}\sin\text{x}^2}{\cos\text{x}^2}$
$\frac{\text{dy}}{\text{dx}}=-2\text{x}\tan\text{x}^2$
Therefore,
$\frac{\text{dy}}{\text{dx}}=-2\text{x}\tan\text{x}^2$

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