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

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

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

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

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derivative of

f (x) = 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_{0}^{1} \frac{14}{4 y - 1} d y

\frac{d}{d p} (ln (p))

\int x x - 3 d x

\int x^{2} 5 x + 7 d x

\frac{d}{d x} (\frac{6 x}{x ^{2} + 9})

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