What is the derivative of f(x)=(sec(x))/(8+sec(x)) ?

The derivative of f(x)=(sec(x))/(8+sec(x)) is (8sec(x)tan(x))/((8+sec(x))^2)

What is the first derivative of f(x)=(sec(x))/(8+sec(x)) ?

The first derivative of f(x)=(sec(x))/(8+sec(x)) is (8sec(x)tan(x))/((8+sec(x))^2)

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derivative of

f (x) = \frac{sec ( x )}{8 + sec ( x )}

\frac{8 sec ( x ) tan ( x )}{( 8 + sec ( x ) ) ^{2}}

Solution steps

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

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

\frac{d}{d x} (8 + sec (x)) = sec (x) tan (x)

= \frac{sec ( x ) tan ( x ) ( 8 + sec ( x ) ) - sec ( x ) tan ( x ) sec ( x )}{( 8 + sec ( x ) ) ^{2}}

Simplify

\frac{sec ( x ) tan ( x ) ( 8 + sec ( x ) ) - sec ( x ) tan ( x ) sec ( x )}{( 8 + sec ( x ) ) ^{2}} : \frac{8 sec ( x ) tan ( x )}{( 8 + sec ( x ) ) ^{2}}

= \frac{8 sec ( x ) tan ( x )}{( 8 + sec ( x ) ) ^{2}}

\int \frac{1}{x ^{3} x ^{2} - 100} d x

\frac{d}{d x} (3 x^{3} e^{- x})

f (x) = 3 x e^{2 x}

\frac{d}{d t} (\frac{1}{1 + t ^{2}})

x \to 3 lim (5^{x})

What is the derivative of f(x)=(sec(x))/(8+sec(x)) ?
The derivative of f(x)=(sec(x))/(8+sec(x)) is (8sec(x)tan(x))/((8+sec(x))^2)
What is the first derivative of f(x)=(sec(x))/(8+sec(x)) ?
The first derivative of f(x)=(sec(x))/(8+sec(x)) is (8sec(x)tan(x))/((8+sec(x))^2)