Question Number 96041 by mhmd last updated on 29/May/20
$${if}\:{f}\left({x}\right)=\mathrm{3}^{{x}^{\mathrm{2}+{x}^{\mathrm{3}} } } \:\:\:{find}\:{f}'\left({x}\right)? \\ $$
Answered by Sourav mridha last updated on 29/May/20
![so,f^′ (x)=ln3.3^x^(2+x^3 ) (d/dx)(e^((2+x^3 ).lnx) ) =ln3.3^x^(2+x^3 ) .x^(2+x^3 ) .[x^2 +(2/x)+3x^2 lnx]](https://www.tinkutara.com/question/Q96049.png)
$$ \\ $$$$\mathrm{so},\mathrm{f}^{'} \left(\mathrm{x}\right)=\mathrm{ln3}.\mathrm{3}^{\mathrm{x}^{\mathrm{2}+\mathrm{x}^{\mathrm{3}} } } \frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{e}^{\left(\mathrm{2}+\mathrm{x}^{\mathrm{3}} \right).\mathrm{lnx}} \right) \\ $$$$\:\:\:\:\:\:=\mathrm{ln3}.\mathrm{3}^{\mathrm{x}^{\mathrm{2}+\mathrm{x}^{\mathrm{3}} } } .\mathrm{x}^{\mathrm{2}+\mathrm{x}^{\mathrm{3}} } .\left[\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{x}}+\mathrm{3x}^{\mathrm{2}} \mathrm{lnx}\right] \\ $$