Question

find nth derivative of y = cos4x

Answer 1

you can see your answer

Answer 2

So, $n^{th}$ Derivative of $y=cos4x$ is $y_{n}=4^{n} cos(\frac{n\pi}{2}+4x)$

Step-by-step explanation:

Given,

Find $n^{th}$ Derivative of $y=cos4x$

Differentiate with respect to $x$,

⇒$\frac{dy}{dx} =\frac{d}{dx} cos4x$

⇒$y_{1}=-4sin4x$

⇒$y_{1}=4cos(\frac{\pi}{2}+4x)$   (∵$cos(\frac{\pi}{2}+4x)=-sin4x$ )

Again differentiate,

⇒$y_{2}=-4\times4 sin(\frac{\pi}{2}+4x)$

⇒$y_{2}=4^{2} cos(\frac{2\pi}{2}+4x)$

Similarly,

⇒$y_{3}=4^{3} cos(\frac{3\pi}{2}+4x)$

∴ $n^{th}$ differentiate is,

∴ $y_{n}=4^{n} cos(\frac{n\pi}{2}+4x)$

∴ $n^{th}$ Derivative of $y=cos4x$ is $y_{n}=4^{n} cos(\frac{n\pi}{2}+4x)$