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

Problem

d()/d(t)*(1/(t−3))2

Solution

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

ƒ(t)=(t−3)(−2)

2. Apply the chain rule, which states that the derivative of un is n*u(n−1)⋅d(u)/d(t)

d(ƒ)/d(t)=−2*(t−3)(−2−1)⋅d(t−3)/d(t)

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

d(t−3)/d(t)=1

4. Substitute the inner derivative back into the expression and simplify the exponent.

d(ƒ)/d(t)=−2*(t−3)(−3)⋅1

5. Convert the expression back into fraction form by moving the negative exponent to the denominator.

d(ƒ)/d(t)=(−2)/((t−3)3)

Final Answer

d()/d(t)*(1/(t−3))2=−2/((t−3)3)

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