What is the derivative of (1-cos(x))/(sin(x)) ?

The derivative of (1-cos(x))/(sin(x)) is 1/(1+cos(x))

What is the first derivative of (1-cos(x))/(sin(x)) ?

The first derivative of (1-cos(x))/(sin(x)) is 1/(1+cos(x))

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derivative of

\frac{1 - cos ( x )}{sin ( x )}

\frac{1}{1 + cos ( x )}

Solution steps

\frac{d}{d x} (\frac{1 - cos ( x )}{sin ( x )})

Simplify

\frac{1 - cos ( x )}{sin ( x )} : - cot (x) + csc (x)

= \frac{d}{d x} (- cot (x) + csc (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (cot (x)) + \frac{d}{d x} (csc (x))

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= - (- csc^{2} (x)) - cot (x) csc (x)

Simplify

- (- csc^{2} (x)) - cot (x) csc (x) : \frac{1}{1 + cos ( x )}

= \frac{1}{1 + cos ( x )}

What is the derivative of (1-cos(x))/(sin(x)) ?
The derivative of (1-cos(x))/(sin(x)) is 1/(1+cos(x))
What is the first derivative of (1-cos(x))/(sin(x)) ?
The first derivative of (1-cos(x))/(sin(x)) is 1/(1+cos(x))