解答 - 导数

应用导数的和法则。

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

一个变量对其本身的导数总是等于一。

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

应用导数的乘法规则。

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

常数的导数总是零。

$$\cos \left(x+2y\right)\times \left(1+\left(\frac{d}{dx}\left[2\right]\times y+2\times \frac{d}{dx}\left[y\right]\right)\right)=\cos \left(x+2y\right)\times \left(1+\left(0y+2\times \frac{d}{dx}\left[y\right]\right)\right)$$

一个数乘以零总是等于零。

$$\cos \left(x+2y\right)\times \left(1+\left(0y+2\times \frac{d}{dx}\left[y\right]\right)\right)=\cos \left(x+2y\right)\times \left(1+\left(0+2\times \frac{d}{dx}\left[y\right]\right)\right)$$

一个数加零，其结果不变。

$$\cos \left(x+2y\right)\times \left(1+\left(0+2\times \frac{d}{dx}\left[y\right]\right)\right)=\cos \left(x+2y\right)\times \left(1+2\times \frac{d}{dx}\left[y\right]\right)$$