Solve 12k^3-27k^2-46k+40

$$12 k ^ { 3 } - 27 k ^ { 2 } - 46 k + 40$$

Differentiate w.r.t. k

$$36k^{2}-54k-46$$

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}.

$$3\times 12k^{3-1}+2\left(-27\right)k^{2-1}-46k^{1-1}$$

Multiply 3 times 12.

$$36k^{3-1}+2\left(-27\right)k^{2-1}-46k^{1-1}$$

Subtract 1 from 3.

$$36k^{2}+2\left(-27\right)k^{2-1}-46k^{1-1}$$

Multiply 2 times -27.

$$36k^{2}-54k^{2-1}-46k^{1-1}$$

Subtract 1 from 2.

$$36k^{2}-54k^{1}-46k^{1-1}$$

Subtract 1 from 1.

$$36k^{2}-54k^{1}-46k^{0}$$

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

$$36k^{2}-54k-46k^{0}$$

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

$$36k^{2}-54k-46$$

Evaluate

$$12k^{3}-27k^{2}-46k+40$$