Q. 345.0( 1 Vote )

# Differentiate each of the following w.r.t. x(sin x)cos x

Given: (Sin x)cos x

To Find: Differentiate w.r.t x

We have (Sin x)cos x

Let y=(Sin x)cos x

Now, Taking Log on both sides, we get

Log y = cos x.log(sin x)

Now, Differentiate both side w.r.t. x By using product rule of differentiation    Substitute the value of y , we get

y’ = (Sin x)cos x[cos x.cot x - sin x (log sinx)]

Hence, y’ = (Sin x)cos x[cos x.cot x - sin x (log sinx)]

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