CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY3 Marks
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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