This is actually pretty easy. It's just that the exponential and logarithmic functions make it seem difficult.
So the function is:
[tex]f(x)=x^2+x^4e^{(-2lnx)}[/tex]
We could rewrite this as:
[tex]f(x)=x^2+} \frac{x^4}{e^{(2lnx)} }[/tex]
Knowing the properties of an exponential raised to a logarithmic function, we could simplify this as:
[tex]f(x)=x^2+} \frac{x^4}{x^2} }[/tex]
How? [tex]2lnx=(lnx)^2[/tex] And [tex]e^{lnx}=x[/tex] Knowing those two properties, we were able to get to this answer.
See? This will be easy from now on.
[tex]f(x)= x^{2} + x^{2} [/tex]
Simplifying:
[tex]f(x)=2 x^{2} [/tex]
Taking the derivative, we get 4x.
Hope that helps.
If you're still having trouble or if there are any errors in my answer, don't hesitate to message me or comment on my profile. Thanks!
