Solve 14+9t^2-t^3

$$14 + 9 t ^ { 2 } - t ^ { 3 }$$

Differentiate w.r.t. t

$$3t\left(6-t\right)$$

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}.

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

Multiply 2 times 9.

$$18t^{2-1}+3\left(-1\right)t^{3-1}$$

Subtract 1 from 2.

$$18t^{1}+3\left(-1\right)t^{3-1}$$

Multiply 3 times -1.

$$18t^{1}-3t^{3-1}$$

Subtract 1 from 3.

$$18t^{1}-3t^{2}$$

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

$$18t-3t^{2}$$

Evaluate

$$14+9t^{2}-t^{3}$$