Find the Derivative Using Chain Rule - d/dt f(t)=-5t^2+48t+25

Problem

d()/d(t)*(−5*t2+48*t+25)

Solution

1. Identify the function as a sum of power terms where the variable is t

2. Apply the power rule to the first term, −5*t2 by multiplying the exponent by the coefficient and decreasing the exponent by one.

3. Apply the power rule to the second term, 48*t which results in the constant coefficient.

4. Apply the constant rule to the third term, 25 which results in zero.

5. Simplify the resulting expression to find the derivative.

Final Answer

d()/d(t)*(−5*t2+48*t+25)=−10*t+48

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