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(3x)^1/4
The derivative of the function/ (3x)^1/4

Derivative of (3x)^1/4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
4 _____
\/ 3*x
$$\sqrt[4]{3 x}$$ 
d /4 _____\
--\\/ 3*x /
dx
$$\frac{d}{d x} \sqrt[4]{3 x}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    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:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
4 ___ 4 ___
\/ 3 *\/ x 
-----------
    4*x
$$\frac{\sqrt[4]{3} \sqrt[4]{x}}{4 x}$$
Simplify
The second derivative [src] 
   4 ___
-3*\/ 3 
--------
    7/4 
16*x
$$- \frac{3 \cdot \sqrt[4]{3}}{16 x^{\frac{7}{4}}}$$
Simplify
The third derivative [src] 
   4 ___
21*\/ 3 
--------
    11/4
64*x
$$\frac{21 \cdot \sqrt[4]{3}}{64 x^{\frac{11}{4}}}$$
Simplify
The graph
Derivative of (3x)^1/4
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