Penyelesaian - Derivative

Applying the sum rule of derivatives.

$$\cos \left(2x+3333\right)\times \frac{d}{dx}[2x+3333]=\cos \left(2x+3333\right)\times \left(\frac{d}{dx}\left[2x\right]+\frac{d}{dx}\left[3333\right]\right)$$

Applying the product rule of derivatives.

$$\cos \left(2x+3333\right)\times \left(\frac{d}{dx}\left[2x\right]+\frac{d}{dx}\left[3333\right]\right)=\cos \left(2x+3333\right)\times \left(\left(\frac{d}{dx}\left[2\right]\times x+2\times \frac{d}{dx}\left[x\right]\right)+\frac{d}{dx}\left[3333\right]\right)$$

The derivative of a constant value is always zero.

$$\cos \left(2x+3333\right)\times \left(\left(\frac{d}{dx}\left[2\right]\times x+2\times \frac{d}{dx}\left[x\right]\right)+\frac{d}{dx}\left[3333\right]\right)=\cos \left(2x+3333\right)\times \left(\left(0x+2\times \frac{d}{dx}\left[x\right]\right)+\frac{d}{dx}\left[3333\right]\right)$$

Multiplying a number by zero always results in zero.

$$\cos \left(2x+3333\right)\times \left(\left(0x+2\times \frac{d}{dx}\left[x\right]\right)+\frac{d}{dx}\left[3333\right]\right)=\cos \left(2x+3333\right)\times \left(\left(0+2\times \frac{d}{dx}\left[x\right]\right)+\frac{d}{dx}\left[3333\right]\right)$$

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

$$\cos \left(2x+3333\right)\times \left(\left(0+2\times \frac{d}{dx}\left[x\right]\right)+\frac{d}{dx}\left[3333\right]\right)=\cos \left(2x+3333\right)\times \left(2\times \frac{d}{dx}\left[x\right]+\frac{d}{dx}\left[3333\right]\right)$$

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

$$\cos \left(2x+3333\right)\times \left(2\times \frac{d}{dx}\left[x\right]+\frac{d}{dx}\left[3333\right]\right)=\cos \left(2x+3333\right)\times \left(2\times 1+\frac{d}{dx}\left[3333\right]\right)$$

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

$$\cos \left(2x+3333\right)\times \left(2\times 1+\frac{d}{dx}\left[3333\right]\right)=\cos \left(2x+3333\right)\times \left(2+\frac{d}{dx}\left[3333\right]\right)$$

The derivative of a constant value is always zero.

$$\cos \left(2x+3333\right)\times \left(2+\frac{d}{dx}\left[3333\right]\right)=\cos \left(2x+3333\right)\times \left(2+0\right)$$

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

$$\cos \left(2x+3333\right)\times \left(2+0\right)=\cos \left(2x+3333\right)\times 2$$

Simplifying the arithmetic expressions.

$$\cos \left(2x+3333\right)\times 2=2\cos \left(2x+3333\right)$$