Expert answers to "Calculating derivatives Find the derivative of the following..." - Plainmath

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Answered question

2021-12-05

Calculating derivatives Find the derivative of the following functions.

y = \sec x + \csc x

Answer & Explanation

Michele Tipton

Beginner2021-12-06Added 11 answers

Step 1
Given function is

y = \sec x + \csc x

.
To find derivative of the given function.
Solution:
We know that,

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

Differentiating the given function with respect to x,

\frac{d y}{d x} = \frac{d}{d x} [\sec x + \csc x]

= \frac{d}{d x} (\sec x) + \frac{d}{d x} (\csc x)

= \sec x \tan x + (- \cot x \csc x)

= \sec x \tan x - \cot x \csc x

Step 2
Hence,

\frac{d y}{d x} = \sec x \tan x - \cot x \csc x

.

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