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

Problem

d()/d(t)−1/((2+t)2)

Solution

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

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

3. Differentiate the inner function 2+t with respect to t

d(2+t)/d(t)=1

4. Simplify the expression by multiplying the constants and converting the negative exponent back into a fraction.

2*(2+t)(−3)⋅1=2/((2+t)3)

Final Answer

d()/d(t)−1/((2+t)2)=2/((2+t)3)

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