Solve 2x/12/5

$$2 \frac { x } { 12 } / 5$$

Evaluate

$$\frac{x}{30}$$

Solution Steps

Cancel out 12, the greatest common factor in 2 and 12.

$$\frac{\frac{x}{6}}{5}$$

Express \frac{\frac{x}{6}}{5} as a single fraction.

$$\frac{x}{6\times 5}$$

Multiply 6 and 5 to get 30.

$$\frac{x}{30}$$

Differentiate w.r.t. x

$$\frac{1}{30} = 0.03333333333333333$$

Steps Using Definition of a Derivative

Cancel out 12, the greatest common factor in 2 and 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{6}}{5})$$

Express \frac{\frac{x}{6}}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{6\times 5})$$

Multiply 6 and 5 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{30})$$

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

$$\frac{1}{30}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{30}x^{0}$$

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

$$\frac{1}{30}\times 1$$

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

$$\frac{1}{30}$$