Question

Differentiate the following w.r.t. $x$.
${\tan }^{3}x$.

• A. $\left(3ta{n}^{2}x\right)$
• B. $\left(3ta{n}^{2}x\right)\left(se{c}^{2}x\right)$
• C. $\left(ta{n}^{2}x\right)\left(se{c}^{2}x\right)$
• D. $\left(ta{n}^{2}x\right)\left(si{n}^{2}x\right)$

Answer 1

Answer: (B)

$\left(3ta{n}^{2}x\right)\left(se{c}^{2}x\right)$

$\frac{d}{dx}{\tan }^{3}x$

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

$=3{\tan }^{2}x{\sec }^{2}x$