Penyelesaian - Derivative

Applying the sum rule of derivatives.

$$\frac{d}{dx}[x^5+3x]=\frac{d}{dx}\left[x^5\right]+\frac{d}{dx}\left[3x\right]$$

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

$$\frac{d}{dx}\left[x^5\right]+\frac{d}{dx}\left[3x\right]=5x^{5-1}+\frac{d}{dx}\left[3x\right]$$

Subtracting one from a number.

$$5x^{5-1}+\frac{d}{dx}\left[3x\right]=5x^4+\frac{d}{dx}\left[3x\right]$$

Applying the product rule of derivatives.

$$5x^4+\frac{d}{dx}\left[3x\right]=5x^4+\left(\frac{d}{dx}\left[3\right]\times x+3\times \frac{d}{dx}\left[x\right]\right)$$

The derivative of a constant value is always zero.

$$5x^4+\left(\frac{d}{dx}\left[3\right]\times x+3\times \frac{d}{dx}\left[x\right]\right)=5x^4+\left(0x+3\times \frac{d}{dx}\left[x\right]\right)$$

Multiplying a number by zero always results in zero.

$$5x^4+\left(0x+3\times \frac{d}{dx}\left[x\right]\right)=5x^4+\left(0+3\times \frac{d}{dx}\left[x\right]\right)$$

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

$$5x^4+\left(0+3\times \frac{d}{dx}\left[x\right]\right)=5x^4+3\times \frac{d}{dx}\left[x\right]$$

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

$$5x^4+3\times \frac{d}{dx}\left[x\right]=5x^4+3\times 1$$

Multiplying a number by one, which does not change its value.

$$5x^4+3\times 1=5x^4+3$$