Question

How do you differentiate `f(x)= e^x/(e^(x^2) +2x )` using the quotient rule?

Answer 1

`f^'(x) = (e^x( e^(x^2)+2 x)-e^x(2xe ^(x^2)+2))/( e^(x^2)+2 x)^2`

Explanation:

Quotient rule: `(f/g)^'= (f^' g-f g^')/g^2`

`f(x) = e^x/( e^(x^2)+2 x)`

`f^'(x) = (e^x( e^(x^2)+2 x)-e^x(2xe ^(x^2)+2))/( e^(x^2)+2 x)^2`

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