Differentiate the following function with respect to (x): a +b +c - Vidyadip

Question

Differentiate the following function with respect to $(\text{x})$:$\frac{\text{a}\cos\text{x}+\text{b}\sin\text{x}+\text{c}}{\sin\text{x}}$

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Answer

We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{a}\cos\text{x}+\text{b}\sin\text{x}+\text{c}}{\sin\text{x}}\Big)$
$=\text{a}\frac{\text{d}}{\text{dx}}\Big(\frac{\cos\text{x}}{\sin\text{x}}\Big)+\text{b}\frac{\text{d}}{\text{dx}}(1)+\text{c}\frac{\text{d}}{\text{dx}}\Big(\frac{1}{\sin\text{x}}\Big)$
$=\text{a}(-\text{cosec}^2\text{x})+0+\text{c}(-\text{cosec}\text{x}.\cot\text{x})$
$=-\text{a}\text{cosesc}^2\text{x}-\text{c}\text{cosec}\text{x}.\cot\text{x}$

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