Find the Derivative - d/dt (at^2+bt+c)

Problem

d()/d(t)*(a*t2+b*t+c)

Solution

1. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

d()/d(t)*(a*t2)+d()/d(t)*(b*t)+d()/d(t)*(c)

2. Apply the constant multiple rule to pull the constants a and b out of the derivatives.

ad(t2)/d(t)+bd(t)/d(t)+d(c)/d(t)

3. Apply the power rule to t2 and t and the constant rule to c

a*(2*t)+b(1)+0

4. Simplify the expression by performing the multiplication.

2*a*t+b

Final Answer

d()/d(t)*(a*t2+b*t+c)=2*a*t+b

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