What is the derivative of (sec(x))/(7+sec(x)) ?

The derivative of (sec(x))/(7+sec(x)) is (7sec(x)tan(x))/((7+sec(x))^2)

What is the first derivative of (sec(x))/(7+sec(x)) ?

The first derivative of (sec(x))/(7+sec(x)) is (7sec(x)tan(x))/((7+sec(x))^2)

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derivative of

\frac{sec ( x )}{7 + sec ( x )}

\frac{7 sec ( x ) tan ( x )}{( 7 + sec ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{sec ( x )}{7 + 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 ) ) ( 7 + sec ( x ) ) - \frac{d}{d x} ( 7 + sec ( x ) ) sec ( x )}{( 7 + sec ( x ) ) ^{2}}

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

\frac{d}{d x} (7 + sec (x)) = sec (x) tan (x)

= \frac{sec ( x ) tan ( x ) ( 7 + sec ( x ) ) - sec ( x ) tan ( x ) sec ( x )}{( 7 + sec ( x ) ) ^{2}}

Simplify

\frac{sec ( x ) tan ( x ) ( 7 + sec ( x ) ) - sec ( x ) tan ( x ) sec ( x )}{( 7 + sec ( x ) ) ^{2}} : \frac{7 sec ( x ) tan ( x )}{( 7 + sec ( x ) ) ^{2}}

= \frac{7 sec ( x ) tan ( x )}{( 7 + sec ( x ) ) ^{2}}

y^{^{''}} - 36 y^{^{'}} = 0

\int - 2 e^{- x} x d x

\int \frac{1}{x ^{2} + 1} d x

\int ((x - 2) x + 4) d x

x \to 0 lim (x \cdot (e^{\frac{1}{x}} - 1))

What is the derivative of (sec(x))/(7+sec(x)) ?
The derivative of (sec(x))/(7+sec(x)) is (7sec(x)tan(x))/((7+sec(x))^2)
What is the first derivative of (sec(x))/(7+sec(x)) ?
The first derivative of (sec(x))/(7+sec(x)) is (7sec(x)tan(x))/((7+sec(x))^2)