Solve -7xleft|5right|

$$-7x \left| 5 \right|$$

Evaluate

$$-35x$$

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 5 is 5.

$$-7x\times 5$$

Multiply -7 and 5 to get -35.

$$-35x$$

Differentiate w.r.t. x

$$-35$$

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 5 is 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-7x\times 5)$$

Multiply -7 and 5 to get -35.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-35x)$$

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

$$-35x^{1-1}$$

Subtract 1 from 1.

$$-35x^{0}$$

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

$$-35$$