Differentiate the following function with respect of x: `x^3 \ e^x \ cosx`

Explanation

let `y=x^{3} e^{x} cos x`


differentiating with respect to `x`



`frac{d y}{d x}=frac{d(x^{3} e^{x} cos x)}{d x}`


`frac{d y}{d x}=x^{3} frac{d(e^{x} cos x)}{d x}+e^{x} cos x frac{d}{d x}(x^{3}) `


`frac{d y}{d x}=x^{3}{e^{x}-sin x+cos x e^{x}}+e^{x} cos x .3 x^{2} `


`frac{d y}{d x}=e^{x} x^{2}(-x sin x+x cos x+3 cos x)`