Řešení - Derivative

Computing the derivative of a fraction.

$$\frac{d}{dx}\left[\frac{x^2}{7}\right]=\frac{\frac{d}{dx}\left[x^2\right]\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}$$

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

$$\frac{\frac{d}{dx}\left[x^2\right]\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}=\frac{\left(2x^{2-1}\right)\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}$$

Subtracting one from a number.

$$\frac{\left(2x^{2-1}\right)\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}=\frac{\left(2x^1\right)\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}$$

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

$$\frac{\left(2x^1\right)\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}=\frac{\left(2x\right)\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}$$

The derivative of a constant value is always zero.

$$\frac{\left(2x\right)\times 7-x^2\times \frac{d}{dx}\left[7\right]}{7^2}=\frac{\left(2x\right)\times 7-x^2\times 0}{7^2}$$

Simplifying the arithmetic expressions.

$$\frac{\left(2x\right)\times 7-x^2\times 0}{7^2}=\frac{\left(2x\right)\times 7-x^2\times 0}{49}$$

Multiplying a number by zero always results in zero.

$$\frac{2x\times 7-x^2\times 0}{49}=\frac{2x\times 7+0}{49}$$

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

$$\frac{2x\times 7+0}{49}=\frac{2x\times 7}{49}$$

Simplifying the arithmetic expressions.

$$\frac{2x\times 7}{49}=\frac{14x}{49}$$

Simplifying the arithmetic expressions.

$$\frac{14x}{49}=\frac{2x}{7}$$