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Question

Differentiate the following functions with respect to x:
(x sin x+cos x)(x cos xsin x)

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Solution

We have,

ddx(x sin x+cos x)(x cos xsin x)

We will apply product rule,

=(x cos xsin x)ddx(x sin x+cos x)+(x sin x+cos x)ddx(x cos xsin x)

=(x cos xsin x){ddx(x sin x)+ddx(cos x)}+(x sin x+cos x){ddx(x cos x)ddx(sin x)}

=xn1[n.logxa+1log a]

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