Solve h(x)=-2x^3-4x^2-4x-7

$$h ( x ) = - 2 x ^ { 3 } - 4 x ^ { 2 } - 4 x - 7$$

Differentiate w.r.t. x

$$-6x^{2}-8x-4$$

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}.

$$3\left(-2\right)x^{3-1}+2\left(-4\right)x^{2-1}-4x^{1-1}$$

Multiply 3 times -2.

$$-6x^{3-1}+2\left(-4\right)x^{2-1}-4x^{1-1}$$

Subtract 1 from 3.

$$-6x^{2}+2\left(-4\right)x^{2-1}-4x^{1-1}$$

Multiply 2 times -4.

$$-6x^{2}-8x^{2-1}-4x^{1-1}$$

Subtract 1 from 2.

$$-6x^{2}-8x^{1}-4x^{1-1}$$

Subtract 1 from 1.

$$-6x^{2}-8x^{1}-4x^{0}$$

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

$$-6x^{2}-8x-4x^{0}$$

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

$$-6x^{2}-8x-4$$

Evaluate

$$-2x^{3}-4x^{2}-4x-7$$