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Derivative of $$$1 - \tan{\left(x \right)}$$$

The calculator will find the derivative of $$$1 - \tan{\left(x \right)}$$$, with steps shown.

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Your Input

Find $$$\frac{d}{dx} \left(1 - \tan{\left(x \right)}\right)$$$.

Solution

The derivative of a sum/difference is the sum/difference of derivatives:

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

The derivative of a constant is $$$0$$$:

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

The derivative of the tangent is $$$\frac{d}{dx} \left(\tan{\left(x \right)}\right) = \sec^{2}{\left(x \right)}$$$:

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

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

Answer

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

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function