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

The derivative of (sin(x)/((1+cos(x))^2)) is (cos(x)(cos(x)+1)+2sin^2(x))/((1+cos(x))^3)

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

The first derivative of (sin(x)/((1+cos(x))^2)) is (cos(x)(cos(x)+1)+2sin^2(x))/((1+cos(x))^3)

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

\frac{cos ( x ) ( cos ( x ) + 1 ) + 2 sin ^{2} ( x )}{( 1 + cos ( x ) ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{cos ( x ) ( 1 + cos ( x ) ) ^{2} - ( - 2 sin ( x ) ( 1 + cos ( x ) ) ) sin ( x )}{( ( 1 + cos ( x ) ) ^{2} ) ^{2}} : \frac{cos ( x ) ( cos ( x ) + 1 ) + 2 sin ^{2} ( x )}{( 1 + cos ( x ) ) ^{3}}

= \frac{cos ( x ) ( cos ( x ) + 1 ) + 2 sin ^{2} ( x )}{( 1 + cos ( x ) ) ^{3}}

\frac{d}{d x} (e^{x, x})

\frac{( s + 1 )}{( s ^{2} + s + 10 )}

\int_{4}^{8} 1 - \frac{4}{x} d x

f (x) = 5 x + 4

n = 1 \sum \infty 5^{n}

What is the derivative of (sin(x)/((1+cos(x))^2)) ?
The derivative of (sin(x)/((1+cos(x))^2)) is (cos(x)(cos(x)+1)+2sin^2(x))/((1+cos(x))^3)
What is the first derivative of (sin(x)/((1+cos(x))^2)) ?
The first derivative of (sin(x)/((1+cos(x))^2)) is (cos(x)(cos(x)+1)+2sin^2(x))/((1+cos(x))^3)