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Derivative of:
Derivative of 2^(3*x)
Derivative of -2/x
Derivative of sin(x)*cos(x)
Derivative of 1/cos(x)
Integral of d{x}:
y(x)
x/sqrtx^2-1
y(x)
Identical expressions
y(x)=x/sqrtx^ two - one
y(x) equally x divide by square root of x squared minus 1
y(x) equally x divide by square root of x to the power of two minus one
y(x)=x/√x^2-1
y(x)=x/sqrtx2-1
yx=x/sqrtx2-1
y(x)=x/sqrtx²-1
y(x)=x/sqrtx to the power of 2-1
yx=x/sqrtx^2-1
y(x)=x divide by sqrtx^2-1
Similar expressions
y(x)=x/sqrtx^2+1

The derivative of the function/ y(x)=x/sqrtx^2-1

Derivative of y(x)=x/sqrtx^2-1

The solution

You have entered [src]

  x       
------ - 1
     2    
  ___     
\/ x

$$\frac{x}{\left(\sqrt{x}\right)^{2}} - 1$$

d /  x       \
--|------ - 1|
dx|     2    |
  |  ___     |
  \\/ x      /

$$\frac{d}{d x} \left(\frac{x}{\left(\sqrt{x}\right)^{2}} - 1\right)$$

Transform

Detail solution

Differentiate $\frac{x}{\left(\sqrt{x}\right)^{2}} - 1$ term by term:
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 $g{\left(x \right)} = x$ .
  
  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: $x$ goes to $1$
  Now plug in to the quotient rule:
  
  $0$
2. The derivative of the constant $\left(-1\right) 1$ is zero.
The result is: $0$

The answer is:

$0$

The first derivative [src]

  1      1
------ - -
     2   x
  ___     
\/ x

$$\frac{1}{\left(\sqrt{x}\right)^{2}} - \frac{1}{x}$$

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify