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

Problem

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

Solution

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

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

3. Differentiate the inner function 1+x with respect to x

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

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

−1*(1+x)(−2)⋅1=−1/((1+x)2)

Final Answer

d()/d(x)1/(1+x)=−1/((1+x)2)

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