Řešení - Derivative

Applying the sum rule of derivatives.

$$\frac{d}{dx}[x^2+3]=\frac{d}{dx}\left[x^2\right]+\frac{d}{dx}\left[3\right]$$

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

$$\frac{d}{dx}\left[x^2\right]+\frac{d}{dx}\left[3\right]=2x^{2-1}+\frac{d}{dx}\left[3\right]$$

Subtracting one from a number.

$$2x^{2-1}+\frac{d}{dx}\left[3\right]=2x^1+\frac{d}{dx}\left[3\right]$$

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

$$2x^1+\frac{d}{dx}\left[3\right]=2x+\frac{d}{dx}\left[3\right]$$

The derivative of a constant value is always zero.

$$2x+\frac{d}{dx}\left[3\right]=2x+0$$

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

$$2x+0=2x$$