Řešení - Derivative

Applying the product rule of derivatives.

$$\frac{d}{dx}\left[x^{53}{x}^4\right]=\frac{d}{dx}\left[x^{53}\right]\times x^4+x^{53}\times \frac{d}{dx}\left[x^4\right]$$

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

$$\frac{d}{dx}\left[x^{53}\right]\times x^4+x^{53}\times \frac{d}{dx}\left[x^4\right]=\left(53x^{53-1}\right)\times x^4+x^{53}\times \frac{d}{dx}\left[x^4\right]$$

Subtracting one from a number.

$$\left(53x^{53-1}\right)\times x^4+x^{53}\times \frac{d}{dx}\left[x^4\right]=\left(53x^{52}\right)\times x^4+x^{53}\times \frac{d}{dx}\left[x^4\right]$$

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

$$\left(53x^{52}\right)\times x^4+x^{53}\times \frac{d}{dx}\left[x^4\right]=\left(53x^{52}\right)\times x^4+x^{53}\times \left(4x^{4-1}\right)$$

Subtracting one from a number.

$$\left(53x^{52}\right)\times x^4+x^{53}\times \left(4x^{4-1}\right)=\left(53x^{52}\right)\times x^4+x^{53}\times \left(4x^3\right)$$

Simplifying the arithmetic expressions.

$$53x^{52}\times x^4+x^{53}\times \left(4x^3\right)=53x^{56}+x^{53}\times \left(4x^3\right)$$

Simplifying the arithmetic expressions.

$$53x^{56}+x^{53}\times \left(4x^3\right)=53x^{56}+4x^{56}$$

Simplifying the arithmetic expressions.

$$53x^{56}+4x^{56}=57x^{56}$$