Solve x|7/2

$$x | \frac { 7 } { 2 }$$

Differentiate w.r.t. x

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$

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 \frac{7}{2} is \frac{7}{2}.

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

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

$$\frac{7}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{2}x^{0}$$

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

$$\frac{7}{2}\times 1$$

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

$$\frac{7}{2}$$

Evaluate

$$\frac{7x}{2}$$

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 \frac{7}{2} is \frac{7}{2}.

$$x\times \frac{7}{2}$$