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

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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

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

Simplify

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

\int_{2}^{3} \frac{36}{3 - x} d x

n = 1 \sum \infty \frac{1}{3 n}

x \to - 5 + lim (8)

5 x^{3} - 4 x^{2} + 7 x - 8, at x = 1

\int_{0}^{1} (4 x + 2) e^{2 x} d x

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