find f'(x). anything helps!

also, bonus!
f(x)= e^(2x-1) + e^2

Question

22-05-2017
Mathematics

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find f'(x). anything helps!

also, bonus!
f(x)= e^(2x-1) + e^2

Respuesta :

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jdoe0001 jdoe0001 · Answer 1 · 2017-05-22T23:48:16+02:00

[tex]\bf f(x)=e^{-x}(e^{2x}+x^2)\iff f(x)=e^{-x}e^{2x}+e^{-x}x^2 \\\\\\ f(x)=e^{2x-x}+\cfrac{x^2}{e^x}\implies f(x)=e^x+\cfrac{x^2}{e^x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}\left[ \cfrac{x^2}{e^x} \right]\implies \cfrac{2xe^x-x^2e^x}{(e^x)^2}\implies \cfrac{xe^x(2-x)}{(e^x)(e^x)}\implies \cfrac{x(2-x)}{e^x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=e^x+\cfrac{x(2-x)}{e^x}[/tex]

find f'(x). anything helps! also, bonus! f(x)= e^(2x-1) + e^2

Respuesta :

Otras preguntas

find f'(x). anything helps!

also, bonus!
f(x)= e^(2x-1) + e^2