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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

d er i v a t i v e (2 r a^{r x} + n)^{p}

\frac{d}{d x} (x - 0.8 - 0.2 sin (x))

8 cos^{2} (y) d x + csc^{2} (x) d y = 0, y (\frac{π}{12}) = \frac{π}{4}

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

\frac{d y}{d x} + 4 y = e^{- 4 x}

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