Answer to Question #188151 in Calculus for VPM

Question

1. Differentiate the following functions:

(a) y = x^3 cos

(b) y = e^x/sin 2x

Answer 1

a). y=x³ cos x

${dy\over dx }=f'g + fg'$

Let f = x³ $\implies$ f'=3x²

Let g=cos(x) $\implies$ g' =- sin(x)

$\therefore$ ${dy\over dx}$ = 3x²cos(x)-x³sin(x)

b). $y= {e^x\over sin(2x)}$

${dy\over dx }=$ ${f'g - fg'\over g^2}$

let $f = e^x$ $\implies$ $f' = e^x$

Let $g = sin(2x)$ $\implies$ $g' = 2 cos(2x)$

$\therefore$ ${dy\over dx}=$ ${e^x sin (2x) - e^x 2cos(2x)\over sin ^2 2x}$