Solve -2x|+7

$$- 2 x | + 7$$

Evaluate

$$-14x$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 7 is 7.

$$-2x\times 7$$

Multiply -2 and 7 to get -14.

$$-14x$$

Differentiate w.r.t. x

$$-14$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 7 is 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x\times 7)$$

Multiply -2 and 7 to get -14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-14x)$$

The derivative of ax^{n} is nax^{n-1}.

$$-14x^{1-1}$$

Subtract 1 from 1.

$$-14x^{0}$$

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

$$-14$$