Penyelesaian - Derivative

The derivative of a constant value is always zero.

$$\frac{d}{dx}\left[3\right]\times x\times \frac{4}{x^2}+3\times \frac{d}{dx}\left[x\right]\times \frac{4}{x^2}+3x\times \frac{d}{dx}\left[\frac{4}{x^2}\right]=0x\times \frac{4}{x^2}+3\times \frac{d}{dx}\left[x\right]\times \frac{4}{x^2}+3x\times \frac{d}{dx}\left[\frac{4}{x^2}\right]$$

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

$$0x\times \frac{4}{x^2}+3\times \frac{d}{dx}\left[x\right]\times \frac{4}{x^2}+3x\times \frac{d}{dx}\left[\frac{4}{x^2}\right]=0x\times \frac{4}{x^2}+3\times 1\times \frac{4}{x^2}+3x\times \frac{d}{dx}\left[\frac{4}{x^2}\right]$$

Computing the derivative of a fraction.

$$0x\times \frac{4}{x^2}+3\times 1\times \frac{4}{x^2}+3x\times \frac{d}{dx}\left[\frac{4}{x^2}\right]=0x\times \frac{4}{x^2}+3\times 1\times \frac{4}{x^2}+3x\times \frac{\frac{d}{dx}\left[4\right]\times x^2-4\times \frac{d}{dx}\left[x^2\right]}{{\left(x^2\right)}^2}$$

The derivative of a constant value is always zero.

$$0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{\frac{d}{dx}\left[4\right]\times x^2-4\times \frac{d}{dx}\left[x^2\right]}{{\left(x^2\right)}^2}=0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \frac{d}{dx}\left[x^2\right]}{{\left(x^2\right)}^2}$$

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

$$0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \frac{d}{dx}\left[x^2\right]}{{\left(x^2\right)}^2}=0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x^{2-1}\right)}{{\left(x^2\right)}^2}$$

Subtracting one from a number.

$$0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x^{2-1}\right)}{{\left(x^2\right)}^2}=0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x^1\right)}{{\left(x^2\right)}^2}$$

Any number raised to the power of one equals the number itself.

$$0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x^1\right)}{{\left(x^2\right)}^2}=0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x\right)}{{\left(x^2\right)}^2}$$

Simplifying the arithmetic expressions.

$$0x\times \left(\frac{4}{x^2}\right)+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x\right)}{{\left(x^2\right)}^2}=0+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x\right)}{{\left(x^2\right)}^2}$$

Simplifying the arithmetic expressions.

$$0+3\times 1\times \left(\frac{4}{x^2}\right)+3x\times \frac{0x^2-4\times \left(2x\right)}{{\left(x^2\right)}^2}=0+\frac{12}{x^2}+3x\times \frac{0x^2-4\times \left(2x\right)}{{\left(x^2\right)}^2}$$

Multiplying a number by zero always results in zero.

$$0+\frac{12}{x^2}+3x\times \frac{0x^2-4\times \left(2x\right)}{{\left(x^2\right)}^2}=0+\frac{12}{x^2}+3x\times \frac{0-4\times \left(2x\right)}{{\left(x^2\right)}^2}$$

Simplifying the arithmetic expressions.

$$0+\frac{12}{x^2}+3x\times \frac{0-4\times \left(2x\right)}{{\left(x^2\right)}^2}=0+\frac{12}{x^2}+3x\times \frac{0-4\times \left(2x\right)}{x^4}$$

Adding zero to a number, which does not change its value.

$$0+\frac{12}{x^2}+3x\times \frac{0-4\times \left(2x\right)}{x^4}=\frac{12}{x^2}+3x\times \frac{0-4\times \left(2x\right)}{x^4}$$

Adding zero to a number, which does not change its value.

$$\frac{12}{x^2}+3x\times \frac{0-4\times \left(2x\right)}{x^4}=\frac{12}{x^2}+3x\times \frac{-4\times \left(2x\right)}{x^4}$$

Simplifying the arithmetic expressions.

$$\frac{12}{x^2}+3x\times \frac{-4\times \left(2x\right)}{x^4}=\frac{12}{x^2}+3x\times \frac{-8x}{x^4}$$

Simplifying the arithmetic expressions.

$$\frac{12}{x^2}+3x\times \frac{-8x}{x^4}=\frac{12}{x^2}+3x\times \left(-\frac{8}{x^3}\right)$$

Simplifying the arithmetic expressions.

$$\frac{12}{x^2}+3x\times \left(-\frac{8}{x^3}\right)=\frac{12}{x^2}-\frac{24}{x^2}$$

Simplifying the arithmetic expressions.

$$\frac{12}{x^2}-\frac{24}{x^2}=-\frac{12}{x^2}$$