Question

If $y=sinx,then\frac{d^{3}y}{d{x}^3}atx=\frac{\pi }{2}$ will be

• A. 0.0
• B. 1
• C. -1
• D. $\frac{\pi }{2}$

Answer 1

The correct option is A 0.0

As we discussed in the videos that $\frac{d^{3}y}{d{x}^3}$ is nothing but third successive derivative of y. i.e,
$\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)$
So for the function y = sin x,
$\frac{dy}{dx}=cosx$
$\frac{d}{dx}\left(\frac{dy}{dx}\right)=-sinx$
$\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)=-cosx=\frac{d^{3}y}{d{x}^3}$
At $x=\frac{\pi }{2},$
$\frac{d^{3}y}{d{x}^3}=-cos\frac{\pi }{2}=0$