Solve x^3+75x^2-18x-15

$${ x }^{ 3 } +75 { x }^{ 2 } -18x-15$$

Differentiate w.r.t. x

$$3\left(x^{2}+50x-6\right)$$

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}.

$$3x^{3-1}+2\times 75x^{2-1}-18x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 75x^{2-1}-18x^{1-1}$$

Multiply 2 times 75.

$$3x^{2}+150x^{2-1}-18x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}+150x^{1}-18x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}+150x^{1}-18x^{0}$$

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

$$3x^{2}+150x-18x^{0}$$

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

$$3x^{2}+150x-18$$

Evaluate

$$x^{3}+75x^{2}-18x-15$$