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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d}{d x} ((e^{3 x}) cos (2 x))

\int \frac{3}{5 x} d x

2 x, x^{2} + 3 x - 6

\frac{d}{d x} ((9 x^{2} - 16 x) e^{x})

\frac{1}{t}

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