Answer:
[tex]f'(x)=\frac{2e^{2x}}{(e^{2x}+1)^2}[/tex]
Step-by-step explanation:
We are given that a function
[tex]f(x)=\frac{e^{2x}}{e^{2x}+1}[/tex]
We have to find the derivative of the function
Differentiate w.r.t x
[tex]f'(x)=\frac{2e^{2x}(e^{2x}+1)-2e^{2x}(e^{2x})}{(e^{2x}+1)^2}[/tex]
By using the property
[tex]\frac{d(\frac{u}{v})}{dx}=\frac{u'v-v'u}{v^2}[/tex]
[tex]\frac{d(e^x)}{dx}=e^x[/tex]
[tex]f'(x)=\frac{2e^{4x}+2e^{2x}-2e^{4x}}{(e^{2x}+1)^2}[/tex]
By using property
[tex]a^x\cdot a^y=a^{x+y}[/tex]
[tex]f'(x)=\frac{2e^{2x}}{(e^{2x}+1)^2}[/tex]
