Solve I(t)=(3t^3-4t^2-5t+7)

$$I ( t ) = ( 3 t ^ { 3 } - 4 t ^ { 2 } - 5 t + 7 )$$

Differentiate w.r.t. t

$$9t^{2}-8t-5$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 3t^{3-1}+2\left(-4\right)t^{2-1}-5t^{1-1}$$

Multiply 3 times 3.

$$9t^{3-1}+2\left(-4\right)t^{2-1}-5t^{1-1}$$

Subtract 1 from 3.

$$9t^{2}+2\left(-4\right)t^{2-1}-5t^{1-1}$$

Multiply 2 times -4.

$$9t^{2}-8t^{2-1}-5t^{1-1}$$

Subtract 1 from 2.

$$9t^{2}-8t^{1}-5t^{1-1}$$

Subtract 1 from 1.

$$9t^{2}-8t^{1}-5t^{0}$$

For any term t, t^{1}=t.

$$9t^{2}-8t-5t^{0}$$

For any term t except 0, t^{0}=1.

$$9t^{2}-8t-5$$

Evaluate

$$3t^{3}-4t^{2}-5t+7$$