Question

x⁵ e^x + x⁶ log x

Answer 1

$$\begin{gathered} \frac{d}{dx}\left(x^5{e}^x+x^6\log x\right) \\ =x^5\frac{d}{dx}\left(e^x\right)+e^x\frac{d}{dx}\left(x^5\right)+x^6\frac{d}{dx}\left(\log x\right)+\log x\frac{d}{dx}\left(x^6\right) \\ =x^5{e}^x+e^x\left(5x^4\right)+x^6.\frac{1}{x}+\log x\left(6x^5\right) \\ =x^5{e}^x+e^x\left(5x^4\right)+x^5+\log x\left(6x^5\right) \\ =x^4\left(x{e}^x+5e^x+x+6x\log x\right) \end{gathered}$$