Solve 170/200*100/x

$$\frac{ 170 }{ 200 } \times \frac{ 100 }{ x }$$

Evaluate

$$\frac{85}{x}$$

Solution Steps

Reduce the fraction \frac{170}{200} to lowest terms by extracting and canceling out 10.

$$\frac{17}{20}\times \frac{100}{x}$$

Multiply \frac{17}{20} times \frac{100}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 100}{20x}$$

Cancel out 20 in both numerator and denominator.

$$\frac{5\times 17}{x}$$

Multiply 5 and 17 to get 85.

$$\frac{85}{x}$$

Differentiate w.r.t. x

$$-\frac{85}{x^{2}}$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{170}{200} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{17}{20}\times \frac{100}{x})$$

Multiply \frac{17}{20} times \frac{100}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{17\times 100}{20x})$$

Cancel out 20 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 17}{x})$$

Multiply 5 and 17 to get 85.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{85}{x})$$

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

$$-85x^{-1-1}$$

Subtract 1 from -1.

$$-85x^{-2}$$