Find the Derivative - d/dx 1/(x+3)

Problem

d()/d(x)1/(x+3)

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate using the power rule.

1/(x+3)=(x+3)(−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(x+3)/d(x)=−1*(x+3)(−2)⋅d(x+3)/d(x)

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

d(x+3)/d(x)=1

4. Simplify the expression by multiplying the terms and rewriting the negative exponent as a fraction.

−1*(x+3)(−2)⋅1=−1/((x+3)2)

Final Answer

d()/d(x)1/(x+3)=−1/((x+3)2)

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