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Popular >

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

Solution

derivative of

y = \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

y^{''}+16y^'+64y=t^2e^{-8t}-e^{-8t}

y^{^{''}} + 16 y^{^{'}} + 64 y = t^{2} e^{- 8 t} - e^{- 8 t}

(\partial)/(\partial y)(6xe^{x^2+y^2})

\frac{\partial}{\partial y} (6 x e^{x^{2} + y^{2}})

(\partial)/(\partial y)(x^2e^{x^2y})

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

tangent of ln(x^2-8x+1)(8)tangent of

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derivative of e^x-2sin(x)

\frac{d}{d x} (e^{x} - 2 sin (x))

Frequently Asked Questions (FAQ)

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