Question

If $y=e^{{\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+....\infty }$ then $\frac{dy}{dx}=$

• A. $e^{{\tan }^{2}x}$
• B. $e^{{\tan }^{2}x}{\sec }^{2}x$
• C. $2e^{{\tan }^{2}x}\tan x\cdot {\sec }^{2}x$
• D. $1$

Answer 1

The correct option is C $2e^{{\tan }^{2}x}\tan x\cdot {\sec }^{2}x$

On solving the given G.P on exponent function ,we get,

$y=e^{\frac{si{n}^{2}x}{1-si{n}^{2}x}}$

$y=e^{\frac{si{n}^{2}x}{co{s}^{2}x}}$

$⟹y=e^{ta{n}^{2}x}$

On differentiating, we get

$\frac{dy}{dx}=e^{ta{n}^{2}x}.2tanx.se{c}^{2}x$

$⟹2e^{ta{n}^{2}x}tanx.se{c}^{2}x$