Solve 0.04:0.05:0.06:x

$$0.04 : 0.05 : 0.06 : x$$

Evaluate

$$\frac{40}{3x}$$

Solution Steps

Express \frac{\frac{\frac{0.04}{0.05}}{0.06}}{x} as a single fraction.

$$\frac{\frac{0.04}{0.05}}{0.06x}$$

Expand \frac{0.04}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{4}{5}}{0.06x}$$

Express \frac{\frac{4}{5}}{0.06x} as a single fraction.

$$\frac{4}{5\times 0.06x}$$

Multiply 5 and 0.06 to get 0.3.

$$\frac{4}{0.3x}$$

Differentiate w.r.t. x

$$-\frac{40}{3x^{2}}$$

Steps Using Definition of a Derivative

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

$$-\frac{40}{3}x^{-1-1}$$

Subtract 1 from -1.

$$-\frac{40}{3}x^{-2}$$