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Popular >

derivative of (1-cos(x)/(sin(x)))

Solution

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

Solution

\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 )}

Popular Examples

(\partial}{\partial x}(y+\frac{x^2)/y)

\frac{\partial}{\partial x} (y + \frac{x ^{2}}{y})

derivative of 1/10 x^5-3/4 x^4+4/3 x^3

\frac{d}{d x} (\frac{1}{10} x^{5} - \frac{3}{4} x^{4} + \frac{4}{3} x^{3})

derivative of (x^2+1^3)

\frac{d}{d x} ((x^{2} + 1)^{3})

d/(da)(1+sin(a)+cos(a))

\frac{d}{d a} (1 + sin (a) + cos (a))

derivative of (100(x+25)/x)

\frac{d}{d x} (\frac{100 ( x + 25 )}{x})

Frequently Asked Questions (FAQ)

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))