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# Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

tan3x

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: $\frac{d}{d x}(\tan n u)=\sec ^{2}(n u) \cdot \frac{d}{d x}(n u) .$

Let us take $y=\tan 3 x$

So, by using the above formula, we have

$\frac{d}{d x} \tan 3 x=\sec ^{2}(3 x) \times \frac{d}{d x}(3 x)=3 \sec ^{2}(3 x)$

Differentiation of $y=\tan 3 x$ is $3 \sec ^{2}(3 x)$