คำตอบ - Derivative

Expanding the derivative for multiplication.

$$\frac{d}{dx}\left[4x^{55}{x}^{43}{x}^2\right]=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}\left[4x^{55}{x}^{43}{x}^2\right]=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]$$

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

$$\frac{d}{dx}\left[4x^{55}{x}^{43}{x}^2\right]=\frac{d}{dx}[4\times \left(x^{55}{x}^{43}{x}^2\right)]$$

Applying the product rule of derivatives.

$$\frac{d}{dx}[4\times \left(x^{55}{x}^{43}{x}^2\right)]=\frac{d}{dx}\left[4\right]\times \left(x^{55}{x}^{43}{x}^2\right)+4\times \frac{d}{dx}\left[x^{55}{x}^{43}{x}^2\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}\left[4x^{55}{x}^{43}{x}^2\right]=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}\left[4\right]\times \left(x^{55}{x}^{43}{x}^2\right)+4\times \frac{d}{dx}\left[x^{55}{x}^{43}{x}^2\right]=\frac{d}{dx}\left[4\right]\times \left(x^{55}{x}^{43}{x}^2\right)+4\left(\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)$$

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

$$\frac{d}{dx}\left[x^{55}{x}^{43}{x}^2\right]=\frac{d}{dx}[x^{55}\times \left(x^{43}{x}^2\right)]$$

Applying the product rule of derivatives.

$$\frac{d}{dx}[x^{55}\times \left(x^{43}{x}^2\right)]=\frac{d}{dx}\left[x^{55}\right]\times \left(x^{43}{x}^2\right)+x^{55}\times \frac{d}{dx}\left[x^{43}{x}^2\right]$$

Expanding the derivative for multiplication.

$$\frac{d}{dx}\left[4\right]\times \left(x^{55}{x}^{43}{x}^2\right)+4\times \frac{d}{dx}\left[x^{55}{x}^{43}{x}^2\right]=\frac{d}{dx}\left[4\right]\times \left(x^{55}{x}^{43}{x}^2\right)+4\left(\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)$$

Applying the product rule of derivatives.

$$\frac{d}{dx}\left[x^{43}{x}^2\right]=\frac{d}{dx}\left[x^{43}\right]\times x^2+x^{43}\times \frac{d}{dx}\left[x^2\right]$$

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

$$\frac{d}{dx}\left[x^{55}\right]\times \left(x^{43}{x}^2\right)+x^{55}\left(\frac{d}{dx}\left[x^{43}\right]\times x^2+x^{43}\times \frac{d}{dx}\left[x^2\right]\right)=\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\left(\frac{d}{dx}\left[x^{43}\right]\times x^2+x^{43}\times \frac{d}{dx}\left[x^2\right]\right)$$

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.

$$\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\left(\frac{d}{dx}\left[x^{43}\right]\times x^2+x^{43}\times \frac{d}{dx}\left[x^2\right]\right)=\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+\left(x^{55}\times \left(\frac{d}{dx}\left[x^{43}\right]\times x^2\right)+x^{55}\times \left(x^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)$$

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

$$\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+\left(x^{55}\times \left(\frac{d}{dx}\left[x^{43}\right]\times x^2\right)+x^{55}\times \left(x^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)=\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+\left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}\times \left(x^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)$$

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

$$\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+\left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}\times \left(x^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)=\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+\left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)$$

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

$$\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+\left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)=\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]$$

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

$$\frac{d}{dx}\left[4\right]\times \left(x^{55}{x}^{43}{x}^2\right)+4\left(\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+4\left(\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)$$

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.

$$\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+4\left(\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \left(\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2\right)+4\times \left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2\right)+4\times \left(x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)$$

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

$$\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \left(\frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2\right)+4\times \left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2\right)+4\times \left(x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4\times \left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2\right)+4\times \left(x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)$$

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

$$\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4\times \left(x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2\right)+4\times \left(x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4\times \left(x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)$$

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

$$\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4\times \left(x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)\right)=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)$$

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

$$\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+\left(4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]\right)=\frac{d}{dx}\left[4\right]\times x^{55}{x}^{43}{x}^2+4\times \frac{d}{dx}\left[x^{55}\right]\times x^{43}{x}^2+4x^{55}\times \frac{d}{dx}\left[x^{43}\right]\times x^2+4x^{55}{x}^{43}\times \frac{d}{dx}\left[x^2\right]$$