Find the Derivative - d/d@VAR f(t)=1/(3+t)

Problem

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

Solution

1. Identify the function as a reciprocal or a power of a linear expression, which can be rewritten as ƒ(t)=(3+t)^(−1)

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

3. Differentiate the outer function by bringing down the exponent and subtracting one from it.

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

4. Calculate the derivative of the inner function 3+t which is 1

−1*(3+t)^(−2)⋅1

5. Simplify the expression by moving the negative exponent back to the denominator.

−1/((3+t)^2)

Final Answer

d()/d(t)1/(3+t)=−1/((3+t)^2)

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