Question

Find the derivative of the following function:
f(x)= $x^4(5sinx-3cosx)$

Answer 1

Here

$f\left(x\right)=x^4(5sinx-3cosx)$

$\therefore f^{\prime }\left(x\right)=\frac{d}{dx}\left[x^4\right(5sinx-3cosx\left)\right]$

$=x^4.\frac{d}{dx}(5sinx-3cosx)+(5sinx-3cosx)\frac{d}{dx}\left(x^4\right)$

$=x^4(5cosx+3sinx)+(5sinx-3cosx)\left(4x^3\right)$

$=x^3[5xcosx+3xsinx+20sinx-12cosx]$