What is the derivative of 2/(4-cos(2x)) ?

The derivative of 2/(4-cos(2x)) is -(4sin(2x))/((4-cos(2x))^2)

What is the first derivative of 2/(4-cos(2x)) ?

The first derivative of 2/(4-cos(2x)) is -(4sin(2x))/((4-cos(2x))^2)

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\frac{d}{d x} (\frac{2}{4 - cos ( 2 x )})

- \frac{4 sin ( 2 x )}{( 4 - cos ( 2 x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2}{4 - cos ( 2 x )})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{4 - cos ( 2 x )})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((4 - cos (2 x))^{- 1})

Apply the chain rule:

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

= - \frac{1}{( 4 - cos ( 2 x ) ) ^{2}} \frac{d}{d x} (4 - cos (2 x))

\frac{d}{d x} (4 - cos (2 x)) = 2 sin (2 x)

= 2 (- \frac{1}{( 4 - cos ( 2 x ) ) ^{2}} \cdot 2 sin (2 x))

Simplify

2 (- \frac{1}{( 4 - cos ( 2 x ) ) ^{2}} \cdot 2 sin (2 x)) : - \frac{4 sin ( 2 x )}{( 4 - cos ( 2 x ) ) ^{2}}

= - \frac{4 sin ( 2 x )}{( 4 - cos ( 2 x ) ) ^{2}}

\int \frac{1}{t ln ( t ^{2} )} d t

\int \frac{x ^{3} + 5}{5 x + 3} d x

\frac{d}{d x} (\frac{100 x}{x + 1})

\int (1 + e^{2 x}) sin (3 x) d x

\int x sec (8) x^{2} tan (8) x^{2} d x

What is the derivative of 2/(4-cos(2x)) ?
The derivative of 2/(4-cos(2x)) is -(4sin(2x))/((4-cos(2x))^2)
What is the first derivative of 2/(4-cos(2x)) ?
The first derivative of 2/(4-cos(2x)) is -(4sin(2x))/((4-cos(2x))^2)