What is the derivative of f(x)=1/(sin x)?

Kylee Mathis

Kylee Mathis

Answered question

2023-02-26

What is the derivative of d y d x = - cot x csc x ?

Answer & Explanation

Gerald Dickerson

Gerald Dickerson

Beginner2023-02-27Added 10 answers

Since f ( x ) = 1 sin ( x ) = csc ( x ) , the answer can be written down from memorization that f ( x ) = - csc ( x ) cot ( x ) .
Alternatively, the Quotient Rule can be used:
f ( x ) = sin ( x ) 0 - 1 cos ( x ) sin 2 ( x ) = - cos ( x ) sin 2 ( x )
= - 1 sin ( x ) cos ( x ) sin ( x ) = - csc ( x ) cot ( x )

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