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

The derivative of (sqrt(x)/(cos(x))) is (sec(x))/(2sqrt(x))+sqrt(x)sec(x)tan(x)

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

The first derivative of (sqrt(x)/(cos(x))) is (sec(x))/(2sqrt(x))+sqrt(x)sec(x)tan(x)

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sec (x)

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

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

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

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

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

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

\frac{\partial}{\partial x} (x e^{4 x + 2 y})

\int \frac{1}{6 + 2 x} d x

\frac{d}{d x} ((x^{5} + 2)^{2} (x^{3} + 4)^{4})

n = 4 \sum \infty 3 (- \frac{1}{2})^{n}

\frac{a + x}{a ^{2} + x ^{2}}

What is the derivative of (sqrt(x)/(cos(x))) ?
The derivative of (sqrt(x)/(cos(x))) is (sec(x))/(2sqrt(x))+sqrt(x)sec(x)tan(x)
What is the first derivative of (sqrt(x)/(cos(x))) ?
The first derivative of (sqrt(x)/(cos(x))) is (sec(x))/(2sqrt(x))+sqrt(x)sec(x)tan(x)