Solve 8t^3+7t^2-3t+7

$$8 t ^ { 3 } + 7 t ^ { 2 } - 3 t + 7$$

Differentiate w.r.t. t

$$\left(6t-1\right)\left(4t+3\right)$$

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}.

$$3\times 8t^{3-1}+2\times 7t^{2-1}-3t^{1-1}$$

Multiply 3 times 8.

$$24t^{3-1}+2\times 7t^{2-1}-3t^{1-1}$$

Subtract 1 from 3.

$$24t^{2}+2\times 7t^{2-1}-3t^{1-1}$$

Multiply 2 times 7.

$$24t^{2}+14t^{2-1}-3t^{1-1}$$

Subtract 1 from 2.

$$24t^{2}+14t^{1}-3t^{1-1}$$

Subtract 1 from 1.

$$24t^{2}+14t^{1}-3t^{0}$$

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

$$24t^{2}+14t-3t^{0}$$

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

$$24t^{2}+14t-3$$

Evaluate

$$8t^{3}+7t^{2}-3t+7$$