Solve =(330ton)(1000kg/1ton)/(160g)(frac{1kg{1000g})}xfrac{50text{pieces}}{1text{box}}

$$= \frac { ( 330 ton ) ( \frac { 1000 kg } { 1 ton } ) } { ( 160 g ) ( \frac { 1 k g } { 1000 g } ) } x \frac { 50 \text { pieces } } { 1 \text { box } }$$

Evaluate

$$2062500x$$

Short Solution Steps

Cancel out 1 in both numerator and denominator.

$$\frac{330ton\times \frac{1000kg}{ton}}{160g\times \frac{1kg}{1000g}}x$$

Express 330\times \frac{1000kg}{ton} as a single fraction.

$$\frac{\frac{330\times 1000kg}{ton}ton}{160g\times \frac{1kg}{1000g}}x$$

Cancel out g in both numerator and denominator.

$$\frac{\frac{330\times 1000kg}{ton}ton}{160g\times \frac{k}{1000}}x$$

Express 160\times \frac{k}{1000} as a single fraction.

$$\frac{\frac{330\times 1000kg}{ton}ton}{\frac{160k}{1000}g}x$$

Multiply 330 and 1000 to get 330000.

$$\frac{\frac{330000kg}{ton}ton}{\frac{160k}{1000}g}x$$

Express \frac{330000kg}{ton}t as a single fraction.

$$\frac{\frac{330000kgt}{ton}on}{\frac{160k}{1000}g}x$$

Cancel out t in both numerator and denominator.

$$\frac{\frac{330000gk}{no}on}{\frac{160k}{1000}g}x$$

Express \frac{330000gk}{no}o as a single fraction.

$$\frac{\frac{330000gko}{no}n}{\frac{160k}{1000}g}x$$

Cancel out o in both numerator and denominator.

$$\frac{\frac{330000gk}{n}n}{\frac{160k}{1000}g}x$$

Cancel out n and n.

$$\frac{330000gk}{\frac{160k}{1000}g}x$$

Divide 160k by 1000 to get \frac{4}{25}k.

$$\frac{330000gk}{\frac{4}{25}kg}x$$

Cancel out gk in both numerator and denominator.

$$\frac{330000}{\frac{4}{25}}x$$

Divide 330000 by \frac{4}{25} by multiplying 330000 by the reciprocal of \frac{4}{25}.

$$330000\times \frac{25}{4}x$$

Express 330000\times \frac{25}{4} as a single fraction.

$$\frac{330000\times 25}{4}x$$

Multiply 330000 and 25 to get 8250000.

$$\frac{8250000}{4}x$$

Divide 8250000 by 4 to get 2062500.

$$2062500x$$

Differentiate w.r.t. x

$$2062500$$

Steps Using Definition of a Derivative

Cancel out 1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{330ton\times \frac{1000kg}{ton}}{160g\times \frac{1kg}{1000g}}x)$$

Express 330\times \frac{1000kg}{ton} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330\times 1000kg}{ton}ton}{160g\times \frac{1kg}{1000g}}x)$$

Cancel out g in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330\times 1000kg}{ton}ton}{160g\times \frac{k}{1000}}x)$$

Express 160\times \frac{k}{1000} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330\times 1000kg}{ton}ton}{\frac{160k}{1000}g}x)$$

Multiply 330 and 1000 to get 330000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330000kg}{ton}ton}{\frac{160k}{1000}g}x)$$

Express \frac{330000kg}{ton}t as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330000kgt}{ton}on}{\frac{160k}{1000}g}x)$$

Cancel out t in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330000gk}{no}on}{\frac{160k}{1000}g}x)$$

Express \frac{330000gk}{no}o as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330000gko}{no}n}{\frac{160k}{1000}g}x)$$

Cancel out o in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{330000gk}{n}n}{\frac{160k}{1000}g}x)$$

Cancel out n and n.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{330000gk}{\frac{160k}{1000}g}x)$$

Divide 160k by 1000 to get \frac{4}{25}k.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{330000gk}{\frac{4}{25}kg}x)$$

Cancel out gk in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{330000}{\frac{4}{25}}x)$$

Divide 330000 by \frac{4}{25} by multiplying 330000 by the reciprocal of \frac{4}{25}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(330000\times \frac{25}{4}x)$$

Express 330000\times \frac{25}{4} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{330000\times 25}{4}x)$$

Multiply 330000 and 25 to get 8250000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8250000}{4}x)$$

Divide 8250000 by 4 to get 2062500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2062500x)$$

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

$$2062500x^{1-1}$$

Subtract 1 from 1.

$$2062500x^{0}$$

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

$$2062500\times 1$$

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

$$2062500$$