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The derivative of the function/ arcsec2x/√x

You entered:

arcsec2x/√x

What you mean?

arcsec2*x/(sqrt(x))

arcsec2*x*x/(sqrt(x))

ar(csec2*x)/(sqrt(x))

ar(csec2*x)*x/(sqrt(x))

arcs(ec2*x)/(sqrt(x))

arcs(ec2*x)*x/(sqrt(x))

arcsec2*x*x/(sqrt(x))

Derivative of arcsec2x/√x

The solution

You have entered [src]

arcsec2*x
---------
    ___  
  \/ x

$$\frac{arcsec_{2} x}{\sqrt{x}}$$

d /arcsec2*x\
--|---------|
dx|    ___  |
  \  \/ x   /

$$\frac{\partial}{\partial x} \frac{arcsec_{2} x}{\sqrt{x}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x$ and $g{\left(x \right)} = \sqrt{x}$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x$ goes to $1$
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  Now plug in to the quotient rule:
  
  $\frac{1}{2 \sqrt{x}}$
So, the result is: $\frac{arcsec_{2}}{2 \sqrt{x}}$

The answer is:

$\frac{arcsec_{2}}{2 \sqrt{x}}$

The first derivative [src]

arcsec2
-------
    ___
2*\/ x

$$\frac{arcsec_{2}}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

-arcsec2 
---------
     3/2 
  4*x

$$- \frac{arcsec_{2}}{4 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

3*arcsec2
---------
     5/2 
  8*x

$$\frac{3 arcsec_{2}}{8 x^{\frac{5}{2}}}$$

Simplify