Solve 6x^3-5x^2-14x+42

$$6 x ^ { 3 } - 5 x ^ { 2 } - 14 x + 42$$

Differentiate w.r.t. x

$$18x^{2}-10x-14$$

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}.

$$3\times 6x^{3-1}+2\left(-5\right)x^{2-1}-14x^{1-1}$$

Multiply 3 times 6.

$$18x^{3-1}+2\left(-5\right)x^{2-1}-14x^{1-1}$$

Subtract 1 from 3.

$$18x^{2}+2\left(-5\right)x^{2-1}-14x^{1-1}$$

Multiply 2 times -5.

$$18x^{2}-10x^{2-1}-14x^{1-1}$$

Subtract 1 from 2.

$$18x^{2}-10x^{1}-14x^{1-1}$$

Subtract 1 from 1.

$$18x^{2}-10x^{1}-14x^{0}$$

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

$$18x^{2}-10x-14x^{0}$$

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

$$18x^{2}-10x-14$$

Evaluate

$$6x^{3}-5x^{2}-14x+42$$