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е*exp((3x-1)/2)
The derivative of the function/ е*exp((3x-1)/2)

Derivative of е*exp((3x-1)/2)

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The solution

You have entered [src] 
   3*x - 1
   -------
      2   
E*e
ee3x−12e e^{\frac{3 x - 1}{2}} 
E*exp((3*x - 1)/2)
Detail solution

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

    1. Let u=3x−12u = \frac{3 x - 1}{2}.

    2. The derivative of eue^{u} is itself.

    3. Then, apply the chain rule. Multiply by ddx3x−12\frac{d}{d x} \frac{3 x - 1}{2}:

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

        1. Differentiate 3x−13 x - 1 term by term:

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

            1. Apply the power rule: xx goes to 11

            So, the result is: 33

          2. The derivative of the constant −1-1 is zero.

          The result is: 33

        So, the result is: 32\frac{3}{2}

      The result of the chain rule is:

      3e3x−122\frac{3 e^{\frac{3 x - 1}{2}}}{2}

    So, the result is: 3ee3x−122\frac{3 e e^{\frac{3 x - 1}{2}}}{2}

  2. Now simplify:

    3e3x2+122\frac{3 e^{\frac{3 x}{2} + \frac{1}{2}}}{2}

The answer is:

3e3x2+122\frac{3 e^{\frac{3 x}{2} + \frac{1}{2}}}{2}

The graph
02468-8-6-4-2-1010010000000
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The first derivative [src] 
     3*x - 1
     -------
        2   
3*E*e       
------------
     2
3ee3x−122\frac{3 e e^{\frac{3 x - 1}{2}}}{2}
Simplify
The second derivative [src] 
       1   3*x
     - - + ---
       2    2 
9*E*e         
--------------
      4
9ee3x2−124\frac{9 e e^{\frac{3 x}{2} - \frac{1}{2}}}{4}
Simplify
The third derivative [src] 
        1   3*x
      - - + ---
        2    2 
27*E*e         
---------------
       8
27ee3x2−128\frac{27 e e^{\frac{3 x}{2} - \frac{1}{2}}}{8}
Simplify
The graph
Derivative of е*exp((3x-1)/2)
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