Question
Differentiate the function $\cos \left( {a\cos x + b\sin x} \right)$ w.r.t x for some constant a and b.
$\therefore \frac{{dy}}{{dx}} = - \sin \left( {a\cos x + b\sin x} \right)\frac{d}{{dx}}\left( {a\cos x + b\sin x} \right)$
$\Rightarrow \frac{{dy}}{{dx}} = - \sin \left( {a\cos x + b\sin x} \right)\left( { - a\sin x + b\cos x} \right)$
$\Rightarrow \frac{{dy}}{{dx}} = - \left( { - a\sin x + b\cos x} \right)\sin \left( {a\cos x + b\sin x} \right)$
$\Rightarrow \frac{{dy}}{{dx}} = \left( {a\sin x - b\cos x} \right)\sin \left( {a\cos x + b\sin x} \right)$
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