Derivative of \( \displaystyle - x + \tan{\left(x \right)} \)

Problem 2.11 · medium

1. \[ \frac{d}{d x} \left(- x + \tan{\left(x \right)}\right) \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{d}{d x} \left(- x\right) + \frac{d}{d x} \tan{\left(x \right)} \]
   sumApply the sum rule.✓ Proved
3. \[ = - \frac{d}{d x} x + \frac{d}{d x} \tan{\left(x \right)} \]
   constantApply the constant multiple rule to the first term.✓ Proved
4. \[ = \frac{d}{d x} \tan{\left(x \right)} - 1 \]
   derivativeDifferentiate the first term.✓ Proved
5. \[ = \sec^{2}{\left(x \right)} - 1 \]
   trig algebraDifferentiate the tangent function. Rearrange the terms.✓ Proved