Solve (2x^3+11x^2-4x-48)

$$( 2 x ^ { 3 } + 11 x ^ { 2 } - 4 x - 48 )$$

Differentiate w.r.t. x

$$6x^{2}+22x-4$$

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}.

$$3\times 2x^{3-1}+2\times 11x^{2-1}-4x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+2\times 11x^{2-1}-4x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+2\times 11x^{2-1}-4x^{1-1}$$

Multiply 2 times 11.

$$6x^{2}+22x^{2-1}-4x^{1-1}$$

Subtract 1 from 2.

$$6x^{2}+22x^{1}-4x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}+22x^{1}-4x^{0}$$

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

$$6x^{2}+22x-4x^{0}$$

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

$$6x^{2}+22x-4$$

Evaluate

$$2x^{3}+11x^{2}-4x-48$$