Řešení - Derivative

Applying the product rule of derivatives.

$$\frac{d}{dx}\left[x^{53}x\right]=\frac{d}{dx}\left[x^{53}\right]\times x+x^{53}\times \frac{d}{dx}\left[x\right]$$

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

$$\frac{d}{dx}\left[x^{53}\right]\times x+x^{53}\times \frac{d}{dx}\left[x\right]=\left(53x^{53-1}\right)\times x+x^{53}\times \frac{d}{dx}\left[x\right]$$

Subtracting one from a number.

$$\left(53x^{53-1}\right)\times x+x^{53}\times \frac{d}{dx}\left[x\right]=\left(53x^{52}\right)\times x+x^{53}\times \frac{d}{dx}\left[x\right]$$

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

$$\left(53x^{52}\right)\times x+x^{53}\times \frac{d}{dx}\left[x\right]=\left(53x^{52}\right)\times x+x^{53}\times 1$$

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

$$\left(53x^{52}\right)\times x+x^{53}\times 1=\left(53x^{52}\right)\times x+x^{53}$$

Simplifying the arithmetic expressions.

$$53x^{52}\times x+x^{53}=53x^{53}+x^{53}$$

Simplifying the arithmetic expressions.

$$53x^{53}+x^{53}=54x^{53}$$