Solve 30:32:42:x

$$30 : 32 : 42 : x$$

Evaluate

$$\frac{5}{224x}$$

Solution Steps

Express \frac{\frac{\frac{30}{32}}{42}}{x} as a single fraction.

$$\frac{\frac{30}{32}}{42x}$$

Reduce the fraction \frac{30}{32} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{15}{16}}{42x}$$

Express \frac{\frac{15}{16}}{42x} as a single fraction.

$$\frac{15}{16\times 42x}$$

Multiply 16 and 42 to get 672.

$$\frac{15}{672x}$$

Differentiate w.r.t. x

$$-\frac{5}{224x^{2}}$$

Steps Using Definition of a Derivative

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

$$-\frac{5}{224}x^{-1-1}$$

Subtract 1 from -1.

$$-\frac{5}{224}x^{-2}$$