We have an answer to "Find the derivative of secx."

Lorena Becker

Answered question

2022-11-25

Find the derivative of

s e c x

revessatrP6

Beginner2022-11-26Added 11 answers

s e c x = \frac{1}{\cos x}

\frac{d}{d x} (s e c x) = \frac{d}{d x} (\frac{1}{\cos x})

f' (\frac{u}{v}) = \frac{u' v - u v'}{v^{2}}

u = 1

and

v = \cos x

\Rightarrow u' = 0

v' = - \sin x

f' (\frac{1}{\cos x}) = \frac{0 \times \cos x - 1 \times (- \sin x)}{{(\cos x)}^{2}}

= \frac{0 + \sin x}{\cos^{2} x} = \frac{\sin x}{\cos x} \times \frac{1}{\cos x} = \tan x \cdot s e c x

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