Solve 10800operatorname{seg}[1h/3600operatorname{seg}]=

$$10800 \operatorname { seg } [ \frac { 1 h } { 3600 \operatorname { seg } } ] =$$

Evaluate

$$3h$$

Solution Steps

Cancel out 1 in both numerator and denominator.

$$10800seg\times \frac{h}{3600seg}$$

Express 10800\times \frac{h}{3600seg} as a single fraction.

$$\frac{10800h}{3600seg}seg$$

Cancel out 3600 in both numerator and denominator.

$$\frac{3h}{egs}seg$$

Express \frac{3h}{egs}s as a single fraction.

$$\frac{3hs}{egs}eg$$

Cancel out s in both numerator and denominator.

$$\frac{3h}{eg}eg$$

Express \frac{3h}{eg}e as a single fraction.

$$\frac{3he}{eg}g$$

Cancel out e in both numerator and denominator.

$$\frac{3h}{g}g$$

Cancel out g and g.

$$3h$$

Differentiate w.r.t. h

$$3$$

Steps Using Definition of a Derivative

Cancel out 1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(10800seg\times \frac{h}{3600seg})$$

Express 10800\times \frac{h}{3600seg} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{10800h}{3600seg}seg)$$

Cancel out 3600 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{3h}{egs}seg)$$

Express \frac{3h}{egs}s as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{3hs}{egs}eg)$$

Cancel out s in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{3h}{eg}eg)$$

Express \frac{3h}{eg}e as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{3he}{eg}g)$$

Cancel out e in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{3h}{g}g)$$

Cancel out g and g.

$$\frac{\mathrm{d}}{\mathrm{d}h}(3h)$$

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

$$3h^{1-1}$$

Subtract 1 from 1.

$$3h^{0}$$

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

$$3\times 1$$

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

$$3$$