Solve 6operatorname{cm}x/12cm

$$6 \operatorname { cm } \frac { x } { 12 cm }$$

Evaluate

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

Solution Steps

Express 6\times \frac{x}{12cm} as a single fraction.

$$\frac{6x}{12cm}cm$$

Cancel out 6 in both numerator and denominator.

$$\frac{x}{2cm}cm$$

Express \frac{x}{2cm}c as a single fraction.

$$\frac{xc}{2cm}m$$

Cancel out c in both numerator and denominator.

$$\frac{x}{2m}m$$

Express \frac{x}{2m}m as a single fraction.

$$\frac{xm}{2m}$$

Cancel out m in both numerator and denominator.

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

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Express 6\times \frac{x}{12cm} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x}{12cm}cm)$$

Cancel out 6 in both numerator and denominator.

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

Express \frac{x}{2cm}c as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xc}{2cm}m)$$

Cancel out c in both numerator and denominator.

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

Express \frac{x}{2m}m as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xm}{2m})$$

Cancel out m in both numerator and denominator.

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

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

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

Subtract 1 from 1.

$$\frac{1}{2}x^{0}$$

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

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

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

$$\frac{1}{2}$$