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Derivative of:
Derivative of x^2*sqrt(1-x^2)
Derivative of e^x*x^2
Derivative of (x+3)/(x-3)
Derivative of x^3/(x^2-4)
Identical expressions
one /(sqrt(five -4y))
1 divide by ( square root of (5 minus 4y))
one divide by ( square root of (five minus 4y))
1/(√(5-4y))
1/sqrt5-4y
1 divide by (sqrt(5-4y))
Similar expressions
1/(sqrt(5+4y))

The derivative of the function/ 1/(sqrt(5-4y))

Derivative of 1/(sqrt(5-4y))

The solution

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     1     
-----------
  _________
\/ 5 - 4*y

$$\frac{1}{\sqrt{5 - 4 y}}$$

1/(sqrt(5 - 4*y))

Detail solution

Let $u = \sqrt{5 - 4 y}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d y} \sqrt{5 - 4 y}$ :
1. Let $u = 5 - 4 y$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d y} \left(5 - 4 y\right)$ :
  1. Differentiate $5 - 4 y$ term by term:
    1. The derivative of the constant $5$ is zero.
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $y$ goes to $1$
      So, the result is: $-4$
    The result is: $-4$
  The result of the chain rule is:
  
  $- \frac{2}{\sqrt{5 - 4 y}}$
The result of the chain rule is:

$\frac{2}{\left(5 - 4 y\right)^{\frac{3}{2}}}$

The answer is:

$\frac{2}{\left(5 - 4 y\right)^{\frac{3}{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          2          
---------------------
            _________
(5 - 4*y)*\/ 5 - 4*y

$$\frac{2}{\sqrt{5 - 4 y} \left(5 - 4 y\right)}$$

Simplify

The second derivative [src]

     12     
------------
         5/2
(5 - 4*y)

$$\frac{12}{\left(5 - 4 y\right)^{\frac{5}{2}}}$$

Simplify

The third derivative [src]

    120     
------------
         7/2
(5 - 4*y)

$$\frac{120}{\left(5 - 4 y\right)^{\frac{7}{2}}}$$

Simplify