Solve 9x/6

$$9 \frac { x } { 6 }$$

Evaluate

$$\frac{3x}{2}$$

Solution Steps

Express 9\times \frac{x}{6} as a single fraction.

$$\frac{9x}{6}$$

Divide 9x by 6 to get \frac{3}{2}x.

$$\frac{3}{2}x$$

Differentiate w.r.t. x

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using Definition of a Derivative

Express 9\times \frac{x}{6} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x}{6})$$

Divide 9x by 6 to get \frac{3}{2}x.

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

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

$$\frac{3}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{2}x^{0}$$

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

$$\frac{3}{2}\times 1$$

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

$$\frac{3}{2}$$