Solve 0.2:0.12:0.3:x

$$0.2 : 0.12 : 0.3 : x$$

Evaluate

$$\frac{50}{9x}$$

Solution Steps

Express \frac{\frac{\frac{0.2}{0.12}}{0.3}}{x} as a single fraction.

$$\frac{\frac{0.2}{0.12}}{0.3x}$$

Expand \frac{0.2}{0.12} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{20}{12}}{0.3x}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{5}{3}}{0.3x}$$

Express \frac{\frac{5}{3}}{0.3x} as a single fraction.

$$\frac{5}{3\times 0.3x}$$

Multiply 3 and 0.3 to get 0.9.

$$\frac{5}{0.9x}$$

Differentiate w.r.t. x

$$-\frac{50}{9x^{2}}$$

Steps Using Definition of a Derivative

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

$$-\frac{50}{9}x^{-1-1}$$

Subtract 1 from -1.

$$-\frac{50}{9}x^{-2}$$