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

The derivative of 1/(1-cos(x)) is -(sin(x))/((1-cos(x))^2)

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

The first derivative of 1/(1-cos(x)) is -(sin(x))/((1-cos(x))^2)

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

- \frac{sin ( x )}{( 1 - cos ( x ) ) ^{2}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((1 - cos (x))^{- 1})

Apply the chain rule:

- \frac{1}{( 1 - cos ( x ) ) ^{2}} \frac{d}{d x} (1 - cos (x))

= - \frac{1}{( 1 - cos ( x ) ) ^{2}} \frac{d}{d x} (1 - cos (x))

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

= - \frac{1}{( 1 - cos ( x ) ) ^{2}} sin (x)

Simplify

- \frac{1}{( 1 - cos ( x ) ) ^{2}} sin (x) : - \frac{sin ( x )}{( 1 - cos ( x ) ) ^{2}}

= - \frac{sin ( x )}{( 1 - cos ( x ) ) ^{2}}

\int \frac{2 x}{x ^{2} - 4 x + 13} d x

\frac{d}{d x} (x e^{x} cot (x))

\frac{d}{d x} (- 10 x + 3 cos (x))

\frac{d ^{2}}{d x ^{2}} ((2 x + 5)^{7})

\int_{1}^{4} (\frac{4}{x} - \frac{16}{x ^{2}}) d x

What is the derivative of 1/(1-cos(x)) ?
The derivative of 1/(1-cos(x)) is -(sin(x))/((1-cos(x))^2)
What is the first derivative of 1/(1-cos(x)) ?
The first derivative of 1/(1-cos(x)) is -(sin(x))/((1-cos(x))^2)