Solve 2t^3-15t^2+36t+10

$$2 t ^ { 3 } - 15 t ^ { 2 } + 36 t + 10$$

Differentiate w.r.t. t

$$6\left(t-3\right)\left(t-2\right)$$

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}.

$$3\times 2t^{3-1}+2\left(-15\right)t^{2-1}+36t^{1-1}$$

Multiply 3 times 2.

$$6t^{3-1}+2\left(-15\right)t^{2-1}+36t^{1-1}$$

Subtract 1 from 3.

$$6t^{2}+2\left(-15\right)t^{2-1}+36t^{1-1}$$

Multiply 2 times -15.

$$6t^{2}-30t^{2-1}+36t^{1-1}$$

Subtract 1 from 2.

$$6t^{2}-30t^{1}+36t^{1-1}$$

Subtract 1 from 1.

$$6t^{2}-30t^{1}+36t^{0}$$

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

$$6t^{2}-30t+36t^{0}$$

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

$$6t^{2}-30t+36\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6t^{2}-30t+36$$

Evaluate

$$2t^{3}-15t^{2}+36t+10$$