Solve -2x^3+x-7x-3-7x

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

Evaluate

$$-2x^{3}-13x-3$$

Solution Steps

Combine x and -7x to get -6x.

$$-2x^{3}-6x-3-7x$$

Combine -6x and -7x to get -13x.

$$-2x^{3}-13x-3$$

Differentiate w.r.t. x

$$-6x^{2}-13$$

Steps Using Derivative Rule for Sum

Combine x and -7x to get -6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{3}-6x-3-7x)$$

Combine -6x and -7x to get -13x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{3}-13x-3)$$

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}.

$$3\left(-2\right)x^{3-1}-13x^{1-1}$$

Multiply 3 times -2.

$$-6x^{3-1}-13x^{1-1}$$

Subtract 1 from 3.

$$-6x^{2}-13x^{1-1}$$

Subtract 1 from 1.

$$-6x^{2}-13x^{0}$$

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

$$-6x^{2}-13$$