1 - tan(x) 的導數

此計算器將求出 $$$1 - \tan{\left(x \right)}$$$ 的導數，並顯示步驟。

您的輸入

求$$$\frac{d}{dx} \left(1 - \tan{\left(x \right)}\right)$$$。

解答

和/差的導數等於導數的和/差：

$${\color{red}\left(\frac{d}{dx} \left(1 - \tan{\left(x \right)}\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(1\right) - \frac{d}{dx} \left(\tan{\left(x \right)}\right)\right)}$$

常數的導數為$$$0$$$：

$${\color{red}\left(\frac{d}{dx} \left(1\right)\right)} - \frac{d}{dx} \left(\tan{\left(x \right)}\right) = {\color{red}\left(0\right)} - \frac{d}{dx} \left(\tan{\left(x \right)}\right)$$

正切函數的導數為 $$$\frac{d}{dx} \left(\tan{\left(x \right)}\right) = \sec^{2}{\left(x \right)}$$$：

$$- {\color{red}\left(\frac{d}{dx} \left(\tan{\left(x \right)}\right)\right)} = - {\color{red}\left(\sec^{2}{\left(x \right)}\right)}$$

因此，$$$\frac{d}{dx} \left(1 - \tan{\left(x \right)}\right) = - \sec^{2}{\left(x \right)}$$$。

答案

$$$\frac{d}{dx} \left(1 - \tan{\left(x \right)}\right) = - \sec^{2}{\left(x \right)}$$$A