Find the derivative of the following function | vedclass

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Question

(A) Let $f(x) = 3 \cot x + 5 \operatorname{cosec} x$. Using the derivative rules:$\frac{d}{dx} [3 \cot x + 5 \operatorname{cosec} x] = 3 \frac{d}{dx}

Vedclass · Accepted Answer

$-3 \operatorname{cosec}^{2} x - 5 \operatorname{cosec} x \cot x$

Vedclass · Answer

(A) Let $f(x) = 3 \cot x + 5 \operatorname{cosec} x$. Using the derivative rules:$\frac{d}{dx} [3 \cot x + 5 \operatorname{cosec} x] = 3 \frac{d}{dx} (\cot x) + 5 \frac{d}{dx} (\operatorname{cosec} x)$We know that $\frac{d}{dx} (\cot x) = -\operatorname{cosec}^{2} x$ and $\frac{d}{dx} (\operatorname{cosec} x) = -\operatorname{cosec} x \cot x$.Substituting these values:$f'(x) = 3(-\operatorname{cosec}^{2} x) + 5(-\operatorname{cosec} x \cot x)$$f'(x) = -3 \operatorname{cosec}^{2} x - 5 \operatorname{cosec} x \cot x$

Find the derivative of the following function: $3 \cot x + 5 \operatorname{cosec} x$

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