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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Simplify

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

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

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

\frac{d}{d x} (3 - 2 x - x^{2})

y = 2 x, y = 2 x - 12, y = 0

\frac{\partial}{\partial x} (2 x z)

\int \frac{1}{- t ^{2} + 8 t - 7} d t

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