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 $-5 \sin 5 x$
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