Řešení - Derivative

Expanding the derivative for multiplication.

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

Expanding the derivative for multiplication.

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

Multiplication can be grouped differently, but the result remains the same.

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

Applying the product rule of derivatives.

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

Expanding the derivative for multiplication.

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

Expanding the derivative for multiplication.

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

Multiplication can be grouped differently, but the result remains the same.

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

Applying the product rule of derivatives.

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

Expanding the derivative for multiplication.

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

Applying the product rule of derivatives.

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

Multiplication can be grouped differently, but the result remains the same.

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

Multiplying a number by a sum or difference of two numbers can be done by multiplying each number individually and then adding or subtracting the results.

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

Multiplication can be grouped differently, but the result remains the same.

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

Multiplication can be grouped differently, but the result remains the same.

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

Addition can be grouped differently, but the result remains the same.

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

Multiplication can be grouped differently, but the result remains the same.

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

Multiplying a number by a sum or difference of two numbers can be done by multiplying each number individually and then adding or subtracting the results.

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

Multiplication can be grouped differently, but the result remains the same.

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

Multiplication can be grouped differently, but the result remains the same.

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

Multiplication can be grouped differently, but the result remains the same.

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

Addition can be grouped differently, but the result remains the same.

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