Řešení - Derivative

Computing the derivative of a power function.

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

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

$$x^x\left(\frac{d}{dx}\left[x\right]\times \ln \left(x\right)+\frac{x}{x}\times \frac{d}{dx}\left[x\right]\right)=x^x\left(1\times \ln \left(x\right)+\frac{x}{x}\times \frac{d}{dx}\left[x\right]\right)$$

Simplifying the arithmetic expressions.

$$x^x\left(1\times \ln \left(x\right)+\frac{x}{x}\times \frac{d}{dx}\left[x\right]\right)=x^x\left(1\times \ln \left(x\right)+1\times \frac{d}{dx}\left[x\right]\right)$$

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

$$x^x\left(1\times \ln \left(x\right)+1\times \frac{d}{dx}\left[x\right]\right)=x^x\left(1\times \ln \left(x\right)+1\times 1\right)$$

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

$$x^x\left(1\times \ln \left(x\right)+1\times 1\right)=x^x\left(\ln \left(x\right)+1\times 1\right)$$

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

$$x^x\left(\ln \left(x\right)+1\times 1\right)=x^x\left(\ln \left(x\right)+1\right)$$

Simplifying the arithmetic expressions.

$$x^x\times \left(\ln \left(x\right)+1\right)=x^x\left(\ln \left(x\right)+1\right)$$