How do you differentiate y=e^x/(1+x) ?

1 Answer
Apr 19, 2018

-e^x/(1+x)^2+e^x/(1+x)

Explanation:

There are a few ways to do this, but the easiest is probably to separate the numerator and denominator into two different fractions. e^x*(1/(1+x))

You can now use the product rule:
d/dxf(x)*g(x)=f'(x)*g(x)+f(x)*g'(x)

The derivative of y=e^x is dy/dx=e^x and the derivative of y=1/(1+x) is dy/dx=-1/(1+x)^2 (You can get this using the power rule.)

From here, just put in the values:

e^x*(-1/(1+x)^2)+(1/(1+x))*e^x

This is pretty messy and doesn't really simplify

-e^x/(1+x)^2+e^x/(1+x)