Solve 2x|-3

$$2 x | - 3$$

Evaluate

$$6x$$

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 -3 is 3.

$$2x\times 3$$

Multiply 2 and 3 to get 6.

$$6x$$

Differentiate w.r.t. x

$$6$$

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 -3 is 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x)$$

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

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

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$