Find the Derivative - d/dx 2/(x+3)

Problem

d()/d(x)2/(x+3)

Solution

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

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

3. Differentiate the inner function x+3

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

4. Simplify the expression by multiplying the constants and the result of the inner derivative.

−2*(x+3)(−2)⋅1=−2*(x+3)(−2)

5. Rewrite the final result using a positive exponent.

−2*(x+3)(−2)=−2/((x+3)2)

Final Answer

d()/d(x)2/(x+3)=−2/((x+3)2)

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