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