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sqrt(x^1/3)*e^2x

How to use it?
Derivative of:
Derivative of 2*sqrt(x)
Derivative of x^2*e^(-x)
Derivative of sin(3*x)
Derivative of cot(x)*cos(x)
Identical expressions
sqrt(x^ one / three)*e^2x
square root of (x to the power of 1 divide by 3) multiply by e squared x
square root of (x to the power of one divide by three) multiply by e squared x
√(x^1/3)*e^2x
sqrt(x1/3)*e2x
sqrtx1/3*e2x
sqrt(x^1/3)*e²x
sqrt(x to the power of 1/3)*e to the power of 2x
sqrt(x^1/3)e^2x
sqrt(x1/3)e2x
sqrtx1/3e2x
sqrtx^1/3e^2x
sqrt(x^1 divide by 3)*e^2x
What you mean?
sqrt(x^(1/3))*e^2*x
sqrt(x^(1/3))*e^(2*x)
sqrt(x^(1/3))*e^(2*x)

The derivative of the function/ sqrt(x^1/3)*e^2x

You entered:

sqrt(x^1/3)*e^2x

What you mean?

sqrt(x^(1/3))*e^2*x

sqrt(x^(1/3))*e^(2*x)

sqrt(x^(1/3))*e^(2*x)

Derivative of sqrt(x^1/3)*e^2x

The solution

You have entered [src]

   _______     
  / 3 ___   2  
\/  \/ x  *e *x

$$x \sqrt{\sqrt[3]{x}} e^{2}$$

  /   _______     \
d |  / 3 ___   2  |
--\\/  \/ x  *e *x/
dx

$$\frac{d}{d x} x \sqrt{\sqrt[3]{x}} e^{2}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x$ goes to $1$
  $g{\left(x \right)} = \sqrt{\sqrt[3]{x}}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Let $u = \sqrt[3]{x}$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt[3]{x}$ :
    1. Apply the power rule: $\sqrt[3]{x}$ goes to $\frac{1}{3 x^{\frac{2}{3}}}$
    The result of the chain rule is:
    
    $\frac{1}{6 x^{\frac{5}{6}}}$
  The result is: $\frac{\sqrt[6]{x}}{6} + \sqrt{\sqrt[3]{x}}$
So, the result is: $\left(\frac{\sqrt[6]{x}}{6} + \sqrt{\sqrt[3]{x}}\right) e^{2}$
Now simplify:

$\frac{7 \sqrt[6]{x} e^{2}}{6}$

The answer is:

$\frac{7 \sqrt[6]{x} e^{2}}{6}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  6 ___  2
7*\/ x *e 
----------
    6

$$\frac{7 \sqrt[6]{x} e^{2}}{6}$$

Simplify

The second derivative [src]

     2 
  7*e  
-------
    5/6
36*x

$$\frac{7 e^{2}}{36 x^{\frac{5}{6}}}$$

Simplify

The third derivative [src]

       2 
  -35*e  
---------
     11/6
216*x

$$- \frac{35 e^{2}}{216 x^{\frac{11}{6}}}$$

Simplify

The graph

Derivative of sqrt(x^1/3)*e^2x