Penyelesaian - Derivative

Computing the derivative of a fraction.

$$\frac{d}{dx}\left[\frac{5}{x}\right]=\frac{\frac{d}{dx}\left[5\right]\times x-5\times \frac{d}{dx}\left[x\right]}{x^2}$$

The derivative of a constant value is always zero.

$$\frac{\frac{d}{dx}\left[5\right]\times x-5\times \frac{d}{dx}\left[x\right]}{x^2}=\frac{0x-5\times \frac{d}{dx}\left[x\right]}{x^2}$$

The derivative of a variable with respect to itself is always equal to one.

$$\frac{0x-5\times \frac{d}{dx}\left[x\right]}{x^2}=\frac{0x-5\times 1}{x^2}$$

Multiplying a number by zero always results in zero.

$$\frac{0x-5\times 1}{x^2}=\frac{0-5\times 1}{x^2}$$

Multiplying a number by one, which does not change its value.

$$\frac{0-5\times 1}{x^2}=\frac{0-5}{x^2}$$

Adding zero to a number, which does not change its value.

$$\frac{0-5}{x^2}=\frac{-5}{x^2}$$

Simplifying the arithmetic expressions.

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