Řešení - Derivative

Computing the derivative of a fraction.

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

The derivative of a constant value is always zero.

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

Computing the derivative of x raised to the power of n.

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

Subtracting one from a number.

$$\frac{0x^2-2\times \left(2x^{2-1}\right)}{{\left(x^2\right)}^2}=\frac{0x^2-2\times \left(2x^1\right)}{{\left(x^2\right)}^2}$$

Any number raised to the power of one equals the number itself.

$$\frac{0x^2-2\times \left(2x^1\right)}{{\left(x^2\right)}^2}=\frac{0x^2-2\times \left(2x\right)}{{\left(x^2\right)}^2}$$

Multiplying a number by zero always results in zero.

$$\frac{0x^2-2\times \left(2x\right)}{{\left(x^2\right)}^2}=\frac{0-2\times \left(2x\right)}{{\left(x^2\right)}^2}$$

Simplifying the arithmetic expressions.

$$\frac{0-2\times \left(2x\right)}{{\left(x^2\right)}^2}=\frac{0-2\times \left(2x\right)}{x^4}$$

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

$$\frac{0-2\times \left(2x\right)}{x^4}=\frac{-2\times \left(2x\right)}{x^4}$$

Simplifying the arithmetic expressions.

$$\frac{-2\times \left(2x\right)}{x^4}=\frac{-4x}{x^4}$$

Simplifying the arithmetic expressions.

$$\frac{-4x}{x^4}=-\frac{4}{x^3}$$