Differentiate the following functions with respect to x: (e^x sin x)/(x^2 + 2)^3

Question

Differentiate the following functions with respect to x:

\(\cfrac{e^\mathrm x sin\, \mathrm x}{(\mathrm x^2+2)^3}\)

Answer 1

Let y =  \(\cfrac{e^\mathrm x sin\, \mathrm x}{(\mathrm x^2+2)^3}\)

On differentiating y with respect to x, we get

We have (uv)’ = vu’ + uv’ (product rule)

However, \(\frac{d}{d\mathrm x}\)(x²) = 2x and derivative of a constant is 0.