Solve -3x^3-x^2-15x+5

$$- 3 x ^ { 3 } - x ^ { 2 } - 15 x + 5$$

Differentiate w.r.t. x

$$-9x^{2}-2x-15$$

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}.

$$3\left(-3\right)x^{3-1}+2\left(-1\right)x^{2-1}-15x^{1-1}$$

Multiply 3 times -3.

$$-9x^{3-1}+2\left(-1\right)x^{2-1}-15x^{1-1}$$

Subtract 1 from 3.

$$-9x^{2}+2\left(-1\right)x^{2-1}-15x^{1-1}$$

Multiply 2 times -1.

$$-9x^{2}-2x^{2-1}-15x^{1-1}$$

Subtract 1 from 2.

$$-9x^{2}-2x^{1}-15x^{1-1}$$

Subtract 1 from 1.

$$-9x^{2}-2x^{1}-15x^{0}$$

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

$$-9x^{2}-2x-15x^{0}$$

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

$$-9x^{2}-2x-15$$

Evaluate

$$5-15x-x^{2}-3x^{3}$$