What is the derivative of y=(sec(x))/(1+sec(x)) ?

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

What is the first derivative of y=(sec(x))/(1+sec(x)) ?

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

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derivative of

y = \frac{sec ( x )}{1 + sec ( x )}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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