Find the Derivative - d/dx y=(e^x-1)/(e^x+1)

Problem

d()/d(x)(ex−1)/(ex+1)

Solution

1. Identify the rule needed for the derivative of a quotient, which is the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator functions: u=ex−1 and v=ex+1

3. Differentiate both parts with respect to x d(ex−1)/d(x)=ex and d(ex+1)/d(x)=ex

4. Substitute these into the quotient rule formula:

d()/d(x)(ex−1)/(ex+1)=((ex+1)*ex−(ex−1)*ex)/((ex+1)2)

5. Distribute the ex in the numerator:

d()/d(x)(ex−1)/(ex+1)=(e(2*x)+ex−(e(2*x)−ex))/((ex+1)2)

6. Simplify the numerator by combining like terms:

d()/d(x)(ex−1)/(ex+1)=(e(2*x)+ex−e(2*x)+ex)/((ex+1)2)

d()/d(x)(ex−1)/(ex+1)=(2*ex)/((ex+1)2)

Final Answer

d()/d(x)(ex−1)/(ex+1)=(2*ex)/((ex+1)2)

Want more problems? Check here!