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

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Answer 1 · 2018-04-19T22:49:33

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

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)#