Let $f ( x ) = \frac { 1 + \cos x } { \sin x }$ Then $f ^ { \prime } ( x )$ is

A)-tan x
B)cot x
C)-cot x - csc x
D)-csc x(cot x + csc x)
E)-csc x(cot x - csc x)

Name: Let $f ( x ) = \frac { 1 + \cos x } { \sin x }$ Then $f ^ { \prime } ( x )$ is A)-tan x B)cot x C)-cot x - csc x D)-csc x(cot x + csc x) E)-csc x(cot x - csc x)
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Question

Let $f ( x ) = \frac { 1 + \cos x } { \sin x }$ Then $f ^ { \prime } ( x )$ is

A)-tan x
B)cot x
C)-cot x - csc x
D)-csc x(cot x + csc x)
E)-csc x(cot x - csc x)

Quizplus · Accepted Answer

To find $f'(x)$, we use the quotient rule and trigonometric identities. The derivative of $f(x) = \frac{1 + \cos x}{\sin x}$ is $f'(x) = -\csc x(\cot x + \csc x)$.

Let f(x)=1+cos⁡xsin⁡xf ( x ) = \frac { 1 + \cos x } { \sin x }f(x)=sinx1+cosx​

Let $f ( x ) = \frac { 1 + \cos x } { \sin x }$