Differentiate the following function with respect to (x): (x+h) - Vidyadip

Question

Differentiate the following function with respect to $(\text{x})$:$\cos(\text{x}+\text{h})$

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Answer

We have,$\frac{\text{d}}{\text{dx}}\Big\{\cos(\text{x}+\text{h})\Big\}$
$=\frac{\text{d}}{\text{dx}}(\cos\text{x}.\cos\text{a}-\sin\text{x}.\sin\text{a})\ [\because\cos(\text{x}+\text{a})=\cos\text{x}\cos\text{a}-\sin\text{x}\sin\text{a}]$
$=\cos\text{a}\frac{\text{d}}{\text{dx}}(\cos\text{x})-\sin\text{a}\frac{\text{d}}{\text{dx}}(\sin\text{x})$
$=\cos\text{a}(-\sin\text{x})-\sin\text{a}(\cos\text{x})$
$=\cos\text{x}(\sin\text{a})+\sin\text{x}(\cos\text{a})$
$=-(\sin\text{x}\cos\text{a}+\cos\text{x}\sin\text{a})$
$=-\sin(\text{x}+\text{a})$

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