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

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Answer 1 · 2018-07-21T17:06:22

#f'(x)=\frac{\cos x(e^x+x)-\sin x(e^x+1)}{(e^x+x)^2}#

The given function"

#f(x)=\frac{\sin x}{e^x+x#

Differentiating above function w.r.t. #x# using quotient rule as follows

#d/dxf(x)=d/dx(\frac{\sin x}{e^x+x})#

#f'(x)=\frac{(e^x+x)d/dx(\sin x)-\sin xd/dx(e^x+x)}{(e^x+x)^2}#

#=\frac{(e^x+x)(\cos x)-\sin x(e^x+1)}{(e^x+x)^2}#

#=\frac{\cos x(e^x+x)-\sin x(e^x+1)}{(e^x+x)^2}#