Řešení - Derivative

Applying the product rule of derivatives.

$$\frac{d}{dx}\left[5x\right]=\frac{d}{dx}\left[5\right]\times x+5\times \frac{d}{dx}\left[x\right]$$

The derivative of a constant value is always zero.

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

Multiplying a number by zero always results in zero.

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

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

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

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

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

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

$$5\times 1=5$$