Solve F(x)=4x^3-3x^2-18x+5

$$F ( x ) = 4 x ^ { 3 } - 3 x ^ { 2 } - 18 x + 5$$

Differentiate w.r.t. x

$$6\left(2x-3\right)\left(x+1\right)$$

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}.

$$3\times 4x^{3-1}+2\left(-3\right)x^{2-1}-18x^{1-1}$$

Multiply 3 times 4.

$$12x^{3-1}+2\left(-3\right)x^{2-1}-18x^{1-1}$$

Subtract 1 from 3.

$$12x^{2}+2\left(-3\right)x^{2-1}-18x^{1-1}$$

Multiply 2 times -3.

$$12x^{2}-6x^{2-1}-18x^{1-1}$$

Subtract 1 from 2.

$$12x^{2}-6x^{1}-18x^{1-1}$$

Subtract 1 from 1.

$$12x^{2}-6x^{1}-18x^{0}$$

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

$$12x^{2}-6x-18x^{0}$$

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

$$12x^{2}-6x-18$$

Evaluate

$$4x^{3}-3x^{2}-18x+5$$