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

The derivative of (sec(x)/x) is (-1+xtan(x))/(x^2cos(x))

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

The first derivative of (sec(x)/x) is (-1+xtan(x))/(x^2cos(x))

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

\frac{- 1 + x tan ( x )}{x ^{2} cos ( 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 x}{d x} sec ( x )}{x ^{2}}

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

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

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

Simplify

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

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

\frac{d}{d x} ((ln (3))^{x})

\int \frac{x}{2} d x

f (x) = 3 x^{2} + 9 x^{3} - 5 x, at x = - 4

\frac{1}{2 ( s + 2 )}

x + 3

What is the derivative of (sec(x)/x) ?
The derivative of (sec(x)/x) is (-1+xtan(x))/(x^2cos(x))
What is the first derivative of (sec(x)/x) ?
The first derivative of (sec(x)/x) is (-1+xtan(x))/(x^2cos(x))