Given:
[tex]f(x)=e^{2x}[/tex]Aim:
We need to differentiate the function f(x).
Explanation:
Differentiate the function f(x).
[tex]\frac{df\mleft(x\mright)}{dx}=\frac{de^{2x}}{dx}[/tex][tex]\text{Use chain rule }\frac{de^{2x}}{dx}=^{}e^{2x}\frac{d(2x)^{}}{dx}\text{.}[/tex][tex]f^{\prime}(x)=e^{2x}\cdot\frac{d(2x)}{dx}[/tex][tex]\text{Use chain rule }\frac{d(2x)^{}}{dx}=2.[/tex][tex]f^{\prime}(x)=e^{2x}\cdot2[/tex][tex]f^{\prime}(x)=2e^{2x}[/tex]Final answer:
[tex]f^{\prime}(x)=2e^{2x}[/tex]