Řešení - Derivative

Computing the derivative of a fraction.

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

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

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

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

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