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}.

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

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.

$$9x^{2}-2x+15\times 1$$

For any term t, t\times 1=t and 1t=t.

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

Evaluate

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