Solve =(330ton)(1.000kg/1ton)/(160g)(frac{1kg{1.000g})}xfrac{50text{pieces}}{1text{box}}

$$= \frac { ( 330 ton ) ( \frac { 1.000 kg } { 1 ton } ) } { ( 160 g ) ( \frac { 1 k g } { 1.000 g } ) } x \frac { 50 \text { pieces } } { 1 \text { box } }$$

Evaluate

$$\frac{33x}{16}$$

Solution Steps

Cancel out 1 in both numerator and denominator.

$$\frac{330ton\times \frac{gk}{not}}{160g\times \frac{1kg}{1g}}x$$

Express 330\times \frac{gk}{not} as a single fraction.

$$\frac{\frac{330gk}{not}ton}{160g\times \frac{1kg}{1g}}x$$

Cancel out g in both numerator and denominator.

$$\frac{\frac{330gk}{not}ton}{160gk}x$$

Express \frac{330gk}{not}t as a single fraction.

$$\frac{\frac{330gkt}{not}on}{160gk}x$$

Cancel out t in both numerator and denominator.

$$\frac{\frac{330gk}{no}on}{160gk}x$$

Express \frac{330gk}{no}o as a single fraction.

$$\frac{\frac{330gko}{no}n}{160gk}x$$

Cancel out o in both numerator and denominator.

$$\frac{\frac{330gk}{n}n}{160gk}x$$

Cancel out n and n.

$$\frac{330gk}{160gk}x$$

Cancel out 10gk in both numerator and denominator.

$$\frac{33}{16}x$$

Differentiate w.r.t. x

$$\frac{33}{16} = 2\frac{1}{16} = 2.0625$$

Steps Using Definition of a Derivative

Cancel out 1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{330ton\times \frac{gk}{not}}{160g\times \frac{1kg}{1g}}x)$$

Express 330\times \frac{gk}{not} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330gk}{not}ton}{160g\times \frac{1kg}{1g}}x)$$

Cancel out g in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330gk}{not}ton}{160gk}x)$$

Express \frac{330gk}{not}t as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330gkt}{not}on}{160gk}x)$$

Cancel out t in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330gk}{no}on}{160gk}x)$$

Express \frac{330gk}{no}o as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330gko}{no}n}{160gk}x)$$

Cancel out o in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330gk}{n}n}{160gk}x)$$

Cancel out n and n.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{330gk}{160gk}x)$$

Cancel out 10gk in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33}{16}x)$$

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

$$\frac{33}{16}x^{1-1}$$

Subtract 1 from 1.

$$\frac{33}{16}x^{0}$$

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

$$\frac{33}{16}\times 1$$

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

$$\frac{33}{16}$$