simplifying the fraction after finding derivative

[coolbeans33]

so I was reading my textbook and was showing steps on applying the quotient rule to the function: y=e^x/(1+x²)

it went from (1+x²)(e^x)-(e^x)(2^x)/(1+x²)²

to e^x(1-x)²/(1+x²)²

I understand the first step, but don't get how they got e^x(1-x)² in the numerator in the second step. can someone please explain this to me?

 

[Deleted member 4993]

so I was reading my textbook and was showing steps on applying the quotient rule to the function: y=e^x/(1+x²)

it went from (1+x²)(e^x)-(e^x)(2^x)/(1+x²)²

to e^x(1-x)²/(1+x²)²

I understand the first step, but don't get how they got e^x(1-x)² in the numerator in the second step. can someone please explain this to me?

That is incorrect.

\(\displaystyle f(x) = \dfrac{e^x}{1+x^2}\)

\(\displaystyle f'(x) = \dfrac{e^x * (1+ x^2) - 2 * x * e^x}{(1+x^2)^2}\)

\(\displaystyle f'(x) = \dfrac{e^x * [1+ x^2 - 2 * x ]}{(1+x^2)^2}\)

Now continue......