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

Derivative of sqrt(4-5x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _________
\/ 4 - 5*x
$$\sqrt{4 - 5 x}$$ 
d /  _________\
--\\/ 4 - 5*x /
dx
$$\frac{d}{d x} \sqrt{4 - 5 x}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        So, the result is:

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     -5      
-------------
    _________
2*\/ 4 - 5*x
$$- \frac{5}{2 \sqrt{4 - 5 x}}$$
Simplify
The second derivative [src] 
     -25      
--------------
           3/2
4*(4 - 5*x)
$$- \frac{25}{4 \left(4 - 5 x\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
    -375      
--------------
           5/2
8*(4 - 5*x)
$$- \frac{375}{8 \left(4 - 5 x\right)^{\frac{5}{2}}}$$
Simplify
3-я производная [src] 
    -375      
--------------
           5/2
8*(4 - 5*x)
$$- \frac{375}{8 \left(4 - 5 x\right)^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of sqrt(4-5x)
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