Solve 9x*1left|2right|

$$9x \times 1 \left| 2 \right|$$

Evaluate

$$18x$$

Solution Steps

Multiply 9 and 1 to get 9.

$$9x|2|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 2 is 2.

$$9x\times 2$$

Multiply 9 and 2 to get 18.

$$18x$$

Differentiate w.r.t. x

$$18$$

Steps Using Definition of a Derivative

Multiply 9 and 1 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x|2|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 2 is 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x\times 2)$$

Multiply 9 and 2 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x)$$

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

$$18x^{1-1}$$

Subtract 1 from 1.

$$18x^{0}$$

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

$$18\times 1$$

For any term t, t\times 1=t and 1t=t.

$$18$$