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

Problem

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

Solution

1. Identify the function as a reciprocal or a power by rewriting the expression using a negative exponent.

1/(1+t)=(1+t)(−1)

2. Apply the power rule and the chain rule, where the outer function is u(−1) and the inner function is u=1+t

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

3. Differentiate the inner function 1+t with respect to t

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

4. Simplify the expression by multiplying the terms and rewriting the negative exponent as a fraction.

−1*(1+t)(−2)⋅1=−1/((1+t)2)

Final Answer

d()/d(t)1/(1+t)=−1/((1+t)2)

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