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The Derivative of Secant


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{$$ \begin{align} {d \over {dx}} \sec\theta &= {d \over {dx}} \left( {1 \over {\cos\theta}} \right) \cr &= \left( {{\cos\theta{d \over{dx}}1 - 1{d \over {dx}}\cos\theta} \over {\cos^2\theta}} \right) \tag{Quotient rule} \cr &= \left( {{\sin\theta} \over {\cos^2\theta}} \right) \cr &= \left( {1 \over {\cos\theta}} \right) \left( {{\sin\theta} \over {\cos\theta}} \right) \cr {d \over {dx}} \sec\theta &= \sec\theta\tan\theta \end{align} $$}

There was a little extra song and dance there to put it in the preferred form.


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Category: Math Calculus Trigonometry


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This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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August 06, 2017

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