Differentiate given problems w.r.t.x.
cos(a cos x+b sin x),for some constants a and b.

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Solution

Let y=cos(a cos x+b sin x)

Differentiating w.r.t x, we get

$\frac{d}{d x} (a c o s x + b s i n x) = - s i n (a c o s x + b s i n x) \frac{d}{d x} (a c o s x + b s i n x)$

=-sin(a cos x + b sin x){-a sin x + b cos x}

=(a sin x-b cos x) sin (a cos x + b sin x)

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