Find the Derivative - d/dt 2t^2+t

Problem

d()/d(t)*(2*t2+t)

Solution

1. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

d()/d(t)*(2*t2+t)=(d(2)*t2)/d(t)+d(t)/d(t)

2. Apply the constant multiple rule to the first term by moving the constant factor outside the derivative.

(d(2)*t2)/d(t)+d(t)/d(t)=2d(t2)/d(t)+d(t)/d(t)

3. Apply the power rule d(tn)/d(t)=n*t(n−1) to both terms.

2*(2*t(2−1))+1*t(1−1)

4. Simplify the exponents and coefficients to find the final expression.

4*t+1

Final Answer

d()/d(t)*(2*t2+t)=4*t+1

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