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Answered question

2021-10-08

Derivatives involving other trigonometric functions Find the derivative of the following functions.

y = \tan x + \cot x

Answer & Explanation

irwchh

Skilled2021-10-09Added 102 answers

Step 1
Given

y = \tan (x) + \cot (x)

By using

\frac{d}{d x} [f (x) + g (x)] = \frac{d}{d x} (f (x)) + \frac{d}{d x} (g (x))

\frac{d}{d x} [\tan (x)] = \sec^{2} (x)

\frac{d}{d x} [\cot (x)] = - \csc^{2} (x)

Step 2
Differentiate

y = \tan (x) + \cot (x)

with respect to x

\frac{d y}{d x} = \frac{d}{d x} [\tan (x) + \cot (x)]

= \frac{d}{d x} [\tan (x)] + \frac{d}{d x} [\cot (x)]

= \sec^{2} (x) - \csc^{2} (x)

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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