Differentiate the following function with respect of `x : x^5e^x+x^6logx`

Explanation

`frac{d}{d x}(x^{5} e^{x}+x^{6} log x)`


`=x^{5} frac{d}{d x}(e^{x})+e^{x} frac{d}{d x}(x^{5})+x^{6} frac{d}{d x}(log x)+log x frac{d}{d x}(x^{6})`


`=x^{5} e^{x}+e^{x}(5 x^{4})+x^{6} cdot frac{1}{x}+log x(6 x^{5})`


`=x^{5} e^{x}+e^{x}(5 x^{4})+x^{5}+log x(6 x^{5})`


`=x^{4}(x e^{x}+5 e^{x}+x+6 x log x)`