Solve 8x^3+12x^2-15x-10

$$8 { x }^{ 3 } +12 { x }^{ 2 } -15x-10$$

Differentiate w.r.t. x

$$24x^{2}+24x-15$$

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}.

$$3\times 8x^{3-1}+2\times 12x^{2-1}-15x^{1-1}$$

Multiply 3 times 8.

$$24x^{3-1}+2\times 12x^{2-1}-15x^{1-1}$$

Subtract 1 from 3.

$$24x^{2}+2\times 12x^{2-1}-15x^{1-1}$$

Multiply 2 times 12.

$$24x^{2}+24x^{2-1}-15x^{1-1}$$

Subtract 1 from 2.

$$24x^{2}+24x^{1}-15x^{1-1}$$

Subtract 1 from 1.

$$24x^{2}+24x^{1}-15x^{0}$$

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

$$24x^{2}+24x-15x^{0}$$

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

$$24x^{2}+24x-15$$

Evaluate

$$8x^{3}+12x^{2}-15x-10$$