What is the derivative of (cos(x)/x+x/(cos(x))) ?

The derivative of (cos(x)/x+x/(cos(x))) is (-xsin(x)-cos(x))/(x^2)+sec(x)+xsec(x)tan(x)

What is the first derivative of (cos(x)/x+x/(cos(x))) ?

The first derivative of (cos(x)/x+x/(cos(x))) is (-xsin(x)-cos(x))/(x^2)+sec(x)+xsec(x)tan(x)

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\frac{d}{d x} (\frac{cos ( x )}{x} + \frac{x}{cos ( x )})

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

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x} + \frac{x}{cos ( x )})

Simplify

\frac{cos ( x )}{x} + \frac{x}{cos ( x )} : \frac{cos ( x )}{x} + x sec (x)

= \frac{d}{d x} (\frac{cos ( x )}{x} + x sec (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{cos ( x )}{x}) + \frac{d}{d x} (x sec (x))

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

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

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

\frac{1}{4 x ^{2} + 1}

x \to 3 - lim (e^{\frac{3}{3 - x}})

x \to 0 + lim (\frac{x ^{2}}{9} - \frac{2}{x})

\int 7^{x} d x

\int \frac{1}{x ^{\frac{1}{2}} + x ^{\frac{3}{2}}} d x

What is the derivative of (cos(x)/x+x/(cos(x))) ?
The derivative of (cos(x)/x+x/(cos(x))) is (-xsin(x)-cos(x))/(x^2)+sec(x)+xsec(x)tan(x)
What is the first derivative of (cos(x)/x+x/(cos(x))) ?
The first derivative of (cos(x)/x+x/(cos(x))) is (-xsin(x)-cos(x))/(x^2)+sec(x)+xsec(x)tan(x)