Find the Derivative - d/dx 2/(x+1)

Problem

d()/d(x)2/(x+1)

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

2/(x+1)=2*(x+1)(−1)

2. Apply the power rule and the chain rule, where the derivative of un is n⋅u(n−1)⋅d(u)/d(x)

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

3. Differentiate the inner function x+1

d(x+1)/d(x)=1

4. Simplify the expression by multiplying the constants and moving the negative exponent back to the denominator.

−2*(x+1)(−2)⋅1=−2/((x+1)2)

Final Answer

d()/d(x)2/(x+1)=−2/((x+1)2)

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