Solve x^21left|8right|

$${ x }^{ 2 } 1 \left| 8 \right|$$

Evaluate

$$8x^{2}$$

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 8 is 8.

$$x^{2}\times 1\times 8$$

Multiply 1 and 8 to get 8.

$$x^{2}\times 8$$

Differentiate w.r.t. x

$$16x$$

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 8 is 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\times 1\times 8)$$

Multiply 1 and 8 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\times 8)$$

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

$$2\times 8x^{2-1}$$

Multiply 2 times 8.

$$16x^{2-1}$$

Subtract 1 from 2.

$$16x^{1}$$

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

$$16x$$