Solve 2x(-2)+8x(-2)+1

$$2 x ( - 2 ) + 8 x ( - 2 ) + 1$$

Evaluate

$$1-20x$$

Solution Steps

Multiply 2 and -2 to get -4.

$$-4x+8x\left(-2\right)+1$$

Multiply 8 and -2 to get -16.

$$-4x-16x+1$$

Combine -4x and -16x to get -20x.

$$-20x+1$$

Differentiate w.r.t. x

$$-20$$

Steps Using Derivative Rule for Sum

Multiply 2 and -2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x+8x\left(-2\right)+1)$$

Multiply 8 and -2 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x-16x+1)$$

Combine -4x and -16x to get -20x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x+1)$$

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}.

$$-20x^{1-1}$$

Subtract 1 from 1.

$$-20x^{0}$$

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

$$-20$$