Find the Derivative - d/dt -1/((3+t)^2)

Problem

d()/d(t)−1/((3+t)2)

Solution

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

−1/((3+t)2)=−(3+t)(−2)

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

d()/d(t)−(3+t)(−2)=−(−2)*(3+t)(−3)⋅d(3+t)/d(t)

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

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

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

2*(3+t)(−3)⋅1=2*(3+t)(−3)

5. Rewrite the final result using a positive exponent.

2*(3+t)(−3)=2/((3+t)3)

Final Answer

d()/d(t)−1/((3+t)2)=2/((3+t)3)

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