Question

Differentiate with respect to x:

$f\left(x\right)=\frac{\sin (x^2+2)}{x^2+3x+4}$

Answer 1

Given $f\left(x\right)=\frac{\sin (x^2+2)}{x^2+3x+4}$

Using quotient rule and chain rule differentiation of given function:

$=\frac{2x\cos (x^2+2)(x^2+3x+4)-(2x+3)\left(\sin \right(x^2+2\left)\right)}{(x^2+3x+4{)}^2}$