Differentiate w.r.t. x the function in Exercise: (a +b ), for som… - Vidyadip

Question

Differentiate w.r.t. x the function in Exercise:
$\cos(\text{a}\cos\text{x}+\text{b}\sin\text{x}),\ $ for some constant a and b.

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Answer

Let $\text{y}=\cos(\text{a}\cos\text{x}+\text{b}\sin\text{x})$By using chain rule, we obtain
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\cos(\text{a}\cos\text{x}+\text{b}\sin\text{x})$ $\Rightarrow\ \frac{\text{dy}}{\text{dx}}=-\sin(\text{a}\cos\text{x}+\text{b}\sin\text{x}).\frac{\text{d}}{\text{dx}}(\text{a}\cos\text{x}+\text{b}\sin\text{x})$ $=-\sin(\text{a}\cos\text{x}+\text{b}\sin\text{x}).[\text{a}(-\sin\text{x})+\text{b}\cos\text{x}]$ $(\text{a}\sin\text{x}-\text{b}\cos\text{x})-\sin(\text{a}\cos\text{x}+\text{b}\sin\text{x})$

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