What is the derivative of sin(sqrt(1+cos(x))) ?

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

What is the first derivative of sin(sqrt(1+cos(x))) ?

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

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derivative of

sin (1 + cos (x))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 20 e^{- 20 x} d x

\int_{3}^{\infty} x e^{- 3 x} d x

f (x) = x

\frac{d}{d x} (\frac{- 2 x}{2 y})

\frac{d}{d x} (\frac{h x}{2} + \frac{k d}{x})

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