What is the derivative of (sec(x)/(sqrt(x))) ?

The derivative of (sec(x)/(sqrt(x))) is (2xsec(x)tan(x)-sec(x))/(2xsqrt(x))

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

The first derivative of (sec(x)/(sqrt(x))) is (2xsec(x)tan(x)-sec(x))/(2xsqrt(x))

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

\frac{2 x sec ( x ) tan ( x ) - sec ( x )}{2 x x}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

Simplify

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

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

What is the derivative of (sec(x)/(sqrt(x))) ?
The derivative of (sec(x)/(sqrt(x))) is (2xsec(x)tan(x)-sec(x))/(2xsqrt(x))
What is the first derivative of (sec(x)/(sqrt(x))) ?
The first derivative of (sec(x)/(sqrt(x))) is (2xsec(x)tan(x)-sec(x))/(2xsqrt(x))