Mister Exam

Derivative of 3e^(2x)

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src]
   2*x
3*e   
3e2x3 e^{2 x}
d /   2*x\
--\3*e   /
dx        
ddx3e2x\frac{d}{d x} 3 e^{2 x}
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=2xu = 2 x.

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

    3. Then, apply the chain rule. Multiply by ddx2x\frac{d}{d x} 2 x:

      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: 22

      The result of the chain rule is:

      2e2x2 e^{2 x}

    So, the result is: 6e2x6 e^{2 x}


The answer is:

6e2x6 e^{2 x}

The graph
02468-8-6-4-2-101005000000000
The first derivative [src]
   2*x
6*e   
6e2x6 e^{2 x}
The second derivative [src]
    2*x
12*e   
12e2x12 e^{2 x}
The third derivative [src]
    2*x
24*e   
24e2x24 e^{2 x}
The graph
Derivative of 3e^(2x)