Mister Exam

Derivative of 2e^(2x)-4e^(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2*x      x
2*e    - 4*e 
$$- 4 e^{x} + 2 e^{2 x}$$
d /   2*x      x\
--\2*e    - 4*e /
dx               
$$\frac{d}{d x} \left(- 4 e^{x} + 2 e^{2 x}\right)$$
Detail solution
  1. Differentiate term by term:

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

      1. Let .

      2. The derivative of is itself.

      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:

      So, the result is:

    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. The derivative of is itself.

        So, the result is:

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     x      2*x
- 4*e  + 4*e   
$$4 e^{2 x} - 4 e^{x}$$
The second derivative [src]
  /        x\  x
4*\-1 + 2*e /*e 
$$4 \cdot \left(2 e^{x} - 1\right) e^{x}$$
The third derivative [src]
  /        x\  x
4*\-1 + 4*e /*e 
$$4 \cdot \left(4 e^{x} - 1\right) e^{x}$$
The graph
Derivative of 2e^(2x)-4e^(x)