Question

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

Answer 1

`d/dx f(x) = ([(2e^(2x)-x ) * e^x] - [e^x *(4 e^(2x) -1)]) / (2e^(2x) -x)^2`

Explanation:

`d/dx f(x) = ([(2e^(2x)-x ) * e^x] - [e^x *(4 e^(2x) -1)]) / (2e^(2x) -x)^2`

Step 1: Bring the denominator up and multiply by the derivative of numerator.
Step 2: Sustract the quantity by the numerator times the derivative of denominator.
Step 3: Divide the whole thing by the denominator squared.