11.(i)   Find the derivative of the following functions: \sin x \cos x

Answers (1)

Given,

f(x)=\sin x \cos x

Now, As we know the product rule of derivative,

\frac{d(y_1y_2)}{dx}=y_1\frac{dy_2}{dx}+y_2\frac{dy_1}{dx}

So, applying the rule here,

\frac{d(\sin x\cos x)}{dx}=\sin x\frac{d\cos x}{dx}+\cos x\frac{d\sin x}{dx}

\frac{d(\sin x\cos x)}{dx}=\sin x(-\sin x)+\cos x (\cos x)

\frac{d(\sin x\cos x)}{dx}=-\sin^2 x+\cos^2 x

\frac{d(\sin x\cos x)}{dx}=\cos 2x

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