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(5-3*x)*e^(2*x)

Derivative of (5-3*x)*e^(2*x)

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

The graph:

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Piecewise:

The solution

You have entered [src]
           2*x
(5 - 3*x)*e   
$$\left(5 - 3 x\right) e^{2 x}$$
d /           2*x\
--\(5 - 3*x)*e   /
dx                
$$\frac{d}{d x} \left(5 - 3 x\right) e^{2 x}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      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. Apply the power rule: goes to

          So, the result is:

        So, the result is:

      The result is:

    ; to find :

    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:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     2*x                2*x
- 3*e    + 2*(5 - 3*x)*e   
$$2 \cdot \left(5 - 3 x\right) e^{2 x} - 3 e^{2 x}$$
The second derivative [src]
               2*x
-4*(-2 + 3*x)*e   
$$- 4 \cdot \left(3 x - 2\right) e^{2 x}$$
The third derivative [src]
               2*x
-4*(-1 + 6*x)*e   
$$- 4 \cdot \left(6 x - 1\right) e^{2 x}$$
The graph
Derivative of (5-3*x)*e^(2*x)