What is the derivative of (2x/(sqrt(sec(x)))) ?

The derivative of (2x/(sqrt(sec(x)))) is (2-xtan(x))/(sqrt(sec(x)))

What is the first derivative of (2x/(sqrt(sec(x)))) ?

The first derivative of (2x/(sqrt(sec(x)))) is (2-xtan(x))/(sqrt(sec(x)))

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\frac{d}{d x} (\frac{2 x}{sec ( x )})

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

Solution steps

\frac{d}{d x} (\frac{2 x}{sec ( x )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

= 2 \cdot \frac{1 \cdot sec ( x ) - \frac{t a n ( x ) s e c ( x )}{2} x}{( sec ( x ) ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot sec ( x ) - \frac{t a n ( x ) s e c ( x )}{2} x}{( sec ( x ) ) ^{2}} : \frac{2 - x tan ( x )}{sec ( x )}

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

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