Differentiate the following with respect to x:

Question:

Differentiate the following with respect to x:

$\tan ^{3} x$

 

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:

$\frac{d}{d x}\left(\tan ^{a} n u\right)=\operatorname{atan}^{a-1} n u \times \frac{d(\tan n u)}{d x} \times \frac{d(n u)}{d x}$ and $\frac{d x^{n}}{d x}=n x^{n-1}$

Let us take $y=\tan ^{3} x$

So, by using the above formula, we have

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

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

 

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