Solve 45:60div27:x

$$45 : 60 \div 27 : x$$

Evaluate

$$\frac{1}{36x}$$

Solution Steps

Express \frac{\frac{\frac{45}{60}}{27}}{x} as a single fraction.

$$\frac{\frac{45}{60}}{27x}$$

Reduce the fraction \frac{45}{60} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{3}{4}}{27x}$$

Express \frac{\frac{3}{4}}{27x} as a single fraction.

$$\frac{3}{4\times 27x}$$

Multiply 4 and 27 to get 108.

$$\frac{3}{108x}$$

Differentiate w.r.t. x

$$-\frac{1}{36x^{2}}$$

Steps Using Definition of a Derivative

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

$$-\frac{1}{36}x^{-1-1}$$

Subtract 1 from -1.

$$-\frac{1}{36}x^{-2}$$