Question

Find the derivative of x^5 logx+x^2.3^x)

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{y}={\mathrm{x}}^5\log \mathrm{x}+{\mathrm{x}}^2.3^{\mathrm{x}} \\ \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}={\mathrm{x}}^5\times \frac{\mathrm{d}}{\mathrm{dx}}\left(\log \mathrm{x}\right)+\log \mathrm{x}\times \frac{\mathrm{d}}{\mathrm{dx}}\left({\mathrm{x}}^5\right)+{\mathrm{x}}^2\times \frac{\mathrm{d}}{\mathrm{dx}}\left(3^{\mathrm{x}}\right)+3^{\mathrm{x}}\times \frac{\mathrm{d}}{\mathrm{dx}}\left({\mathrm{x}}^2\right) \\ \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}={\mathrm{x}}^5\times \frac{1}{\mathrm{x}}+\log \mathrm{x}\times 5{\mathrm{x}}^4+{\mathrm{x}}^2\times 3^{\mathrm{x}}\log 3+3^{\mathrm{x}}.2\mathrm{x} \\ \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}={\mathrm{x}}^4+5{\mathrm{x}}^4\log \mathrm{x}+{\mathrm{x}}^2.3^{\mathrm{x}}\log 3+3^{\mathrm{x}}.2\mathrm{x} \end{gathered}$$