Find the Derivative - d/dt 1/t

Problem

d()/d(t)1/t

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

1/t=t(−1)

2. Apply the power rule for differentiation, which states that d(xn)/d(x)=n*x(n−1)

d(t(−1))/d(t)=−1⋅t(−1−1)

3. Simplify the exponent.

−1⋅t(−2)=−t(−2)

4. Rewrite the result back into fractional form by moving the variable to the denominator.

−t(−2)=−1/(t2)

Final Answer

d()/d(t)1/t=−1/(t2)

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