Find the Derivative - d/dx 1/((x+3)^2)

Problem

d()/d(x)1/((x+3)2)

Solution

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

1/((x+3)2)=(x+3)(−2)

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)=−2*(x+3)(−2−1)⋅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 moving the negative exponent back to the denominator.

−2*(x+3)(−3)⋅1=(−2)/((x+3)3)

Final Answer

d()/d(x)1/((x+3)2)=−2/((x+3)3)

Want more problems? Check here!