Řešení - Derivative

Applying the product rule of derivatives.

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

The derivative of a constant value is always zero.

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

Multiplying a number by zero always results in zero.

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

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

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

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

$$3\times \frac{d}{dx}\left[x^n\right]=3\times \left(n{x}^{n-1}\right)$$

Simplifying the arithmetic expressions.

$$3\times \left(n{x}^{n-1}\right)=3n{x}^{n-1}$$