What is the derivative of 1/(2+cos(x)) ?

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

What is the first derivative of 1/(2+cos(x)) ?

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

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\frac{d}{d x} (\frac{1}{2 + cos ( x )})

\frac{sin ( x )}{( 2 + cos ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{2 + cos ( x )})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d y} (e^{y} y^{e})

\int 4 e^{x} cos (2 x) d x

f (x) = (1 + 3 x) (5 - 2 x), at x = 2

\frac{s}{( s + 1 ) ( s ^{2} + 4 )}

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{10}})

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