Question

find the nth derivative of cos(ax+b)

Answer 1

Answer:

y_n = $a^{n}\times cos[\frac{n\pi}{2} + ax + b]$

Step-by-step explanation:

We can find out the nth derivation of cos (ax + b)

So, Let y = cos (ax + b)

Diffraction both side with respect to x.

y' = $\frac{dy}{dx}$ = $\frac{d}{dx} cos(ax +b)$

  = -a sin(ax + b)

y' = $a\times cos[\frac{\pi}{2} + ax +b]$

Diffraction both side with respect to x.

y'' = $-a^2\times sin[\frac{\pi}{2} + ax +b]$

y'' = $a^{2}\times cos[\frac{2\pi}{2} + ax +b]$

So, y''' = $a^{3}\times cos[\frac{3\pi}{2} + ax +b]$

y'''' = $a^{4}\times cos[\frac{4\pi}{2} + ax +b]$

similarly the value of  nth derivative of cos(ax+b) is

y_n = $a^{n}\times cos[\frac{n\pi}{2} + ax + b]$