คำตอบ - Derivative

Expanding the derivative for multiplication.

$$\frac{d}{dx}[e^c\times osx]=\frac{d}{dx}\left[e^c\right]\times osx+e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times os\times \frac{d}{dx}\left[x\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}[e^c\times osx]=\frac{d}{dx}\left[e^c\right]\times osx+e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times os\times \frac{d}{dx}\left[x\right]$$

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

$$\frac{d}{dx}[e^c\times osx]=\frac{d}{dx}[e^c\times \left(osx\right)]$$

Applying the product rule of derivatives.

$$\frac{d}{dx}[e^c\times \left(osx\right)]=\frac{d}{dx}\left[e^c\right]\times \left(osx\right)+e^c\times \frac{d}{dx}\left[osx\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}[e^c\times osx]=\frac{d}{dx}\left[e^c\right]\times osx+e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times os\times \frac{d}{dx}\left[x\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}\left[e^c\right]\times \left(osx\right)+e^c\times \frac{d}{dx}\left[osx\right]=\frac{d}{dx}\left[e^c\right]\times \left(osx\right)+e^c\times \left(\frac{d}{dx}\left[o\right]\times sx+o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]\right)$$

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

$$\frac{d}{dx}\left[osx\right]=\frac{d}{dx}[o\times \left(sx\right)]$$

Applying the product rule of derivatives.

$$\frac{d}{dx}[o\times \left(sx\right)]=\frac{d}{dx}\left[o\right]\times \left(sx\right)+o\times \frac{d}{dx}\left[sx\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}\left[e^c\right]\times \left(osx\right)+e^c\times \frac{d}{dx}\left[osx\right]=\frac{d}{dx}\left[e^c\right]\times \left(osx\right)+e^c\times \left(\frac{d}{dx}\left[o\right]\times sx+o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]\right)$$

Applying the product rule of derivatives.

$$\frac{d}{dx}\left[sx\right]=\frac{d}{dx}\left[s\right]\times x+s\times \frac{d}{dx}\left[x\right]$$

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

$$\frac{d}{dx}\left[o\right]\times \left(sx\right)+o\left(\frac{d}{dx}\left[s\right]\times x+s\times \frac{d}{dx}\left[x\right]\right)=\frac{d}{dx}\left[o\right]\times sx+o\left(\frac{d}{dx}\left[s\right]\times x+s\times \frac{d}{dx}\left[x\right]\right)$$

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.

$$\frac{d}{dx}\left[o\right]\times sx+o\left(\frac{d}{dx}\left[s\right]\times x+s\times \frac{d}{dx}\left[x\right]\right)=\frac{d}{dx}\left[o\right]\times sx+\left(o\times \left(\frac{d}{dx}\left[s\right]\times x\right)+o\times \left(s\times \frac{d}{dx}\left[x\right]\right)\right)$$

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

$$\frac{d}{dx}\left[o\right]\times sx+\left(o\times \left(\frac{d}{dx}\left[s\right]\times x\right)+o\times \left(s\times \frac{d}{dx}\left[x\right]\right)\right)=\frac{d}{dx}\left[o\right]\times sx+\left(o\times \frac{d}{dx}\left[s\right]\times x+o\times \left(s\times \frac{d}{dx}\left[x\right]\right)\right)$$

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

$$\frac{d}{dx}\left[o\right]\times sx+\left(o\times \frac{d}{dx}\left[s\right]\times x+o\times \left(s\times \frac{d}{dx}\left[x\right]\right)\right)=\frac{d}{dx}\left[o\right]\times sx+\left(o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]\right)$$

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

$$\frac{d}{dx}\left[o\right]\times sx+\left(o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]\right)=\frac{d}{dx}\left[o\right]\times sx+o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]$$

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

$$\frac{d}{dx}\left[e^c\right]\times \left(osx\right)+e^c\times \left(\frac{d}{dx}\left[o\right]\times sx+o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]\right)=\frac{d}{dx}\left[e^c\right]\times osx+e^c\times \left(\frac{d}{dx}\left[o\right]\times sx+o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]\right)$$

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.

$$\frac{d}{dx}\left[e^c\right]\times osx+e^c\times \left(\frac{d}{dx}\left[o\right]\times sx+o\times \frac{d}{dx}\left[s\right]\times x+os\times \frac{d}{dx}\left[x\right]\right)=\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \left(\frac{d}{dx}\left[o\right]\times sx\right)+e^c\times \left(o\times \frac{d}{dx}\left[s\right]\times x\right)+e^c\times \left(os\times \frac{d}{dx}\left[x\right]\right)\right)$$

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

$$\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \left(\frac{d}{dx}\left[o\right]\times sx\right)+e^c\times \left(o\times \frac{d}{dx}\left[s\right]\times x\right)+e^c\times \left(os\times \frac{d}{dx}\left[x\right]\right)\right)=\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times \left(o\times \frac{d}{dx}\left[s\right]\times x\right)+e^c\times \left(os\times \frac{d}{dx}\left[x\right]\right)\right)$$

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

$$\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times \left(o\times \frac{d}{dx}\left[s\right]\times x\right)+e^c\times \left(os\times \frac{d}{dx}\left[x\right]\right)\right)=\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times \left(os\times \frac{d}{dx}\left[x\right]\right)\right)$$

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

$$\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times \left(os\times \frac{d}{dx}\left[x\right]\right)\right)=\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times os\times \frac{d}{dx}\left[x\right]\right)$$

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

$$\frac{d}{dx}\left[e^c\right]\times osx+\left(e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times os\times \frac{d}{dx}\left[x\right]\right)=\frac{d}{dx}\left[e^c\right]\times osx+e^c\times \frac{d}{dx}\left[o\right]\times sx+e^c\times o\times \frac{d}{dx}\left[s\right]\times x+e^c\times os\times \frac{d}{dx}\left[x\right]$$