Question

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

• A. 1
• B. -1
• C. None of the above

Answer 1

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 = sinx,
$\frac{dy}{dx}=cosx$
$\frac{d}{dx}\left(\frac{dy}{dx}\right)=-sinx$
$\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)=-cosx=\frac{d^{3}y}{d{x}^3}$
At $x=\frac{\pi }{2},$
$\frac{d^{3}y}{d{x}^3}=-cos\frac{\pi }{2}=0$ which is the correct answer.