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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\frac{d}{d x} (\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}}

\frac{d}{d x} (ln (x + x^{2} - 8))

d er i v a t i v e \frac{ln ( x )}{x ^{7}}

d er i v a t i v e 7 x^{5} (x^{3} - 6 x)

d er i v a t i v e \frac{x - 6}{x - 6}

\frac{\partial}{\partial x} (5 x^{2} y - 2 x + 3 y^{3})

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)