What is the derivative of 2/(2-cos(pix)) ?

The derivative of 2/(2-cos(pix)) is -(2pisin(pix))/((2-cos(pix))^2)

What is the first derivative of 2/(2-cos(pix)) ?

The first derivative of 2/(2-cos(pix)) is -(2pisin(pix))/((2-cos(pix))^2)

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\frac{d}{d x} (\frac{2}{2 - cos ( π x )})

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

Solution steps

\frac{d}{d x} (\frac{2}{2 - cos ( π x )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 - cos (π x)) = π sin (π x)

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

Simplify

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

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

What is the derivative of 2/(2-cos(pix)) ?
The derivative of 2/(2-cos(pix)) is -(2pisin(pix))/((2-cos(pix))^2)
What is the first derivative of 2/(2-cos(pix)) ?
The first derivative of 2/(2-cos(pix)) is -(2pisin(pix))/((2-cos(pix))^2)