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# Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

cos 5x

Solution:

To Find: Differentiation

NOTE : When 2 functions are in the product then we used product rule i.e

$\frac{d(u, v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$

Formula used: $\frac{d}{d x}(\cos n u)=-\sin (n u) \frac{d}{d x}(n u) .$

Let us take $y=\cos 5 x$.

So, by using the above formula, we have

$\frac{d}{d x}(\cos 5 x)=-\sin (5 x) \times \frac{d}{d x}(5 x)=-5 \sin 5 x$

Differentiation of $y=\cos 5 x$ is $-5 \sin 5 x$