Question

Successively diffrentiate
y=sinx​

Answer 1

Step-by-step explanation:

Successively differentiating we get,

$\frac{dy}{dx} = \cos(x) = \sin( \frac{\pi}{2} + x )$

$= > \frac{ {d}^{2}y }{dx^{2} } = - \sin(x) = \sin(\pi + x)$

$= > \frac{ {d}^{3} y}{d {x}^{3} } = - \cos(x) = \sin( \frac{3\pi}{2} + x )$

So, if n times differentiate this, we will get

$\frac{ {d}^{n}y }{d {x}^{n} } = \sin( \frac{n\pi}{2} + x )$