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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
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The graph:

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The solution

You have entered [src]
           2*x
(5 - 3*x)*e   
(53x)e2x\left(5 - 3 x\right) e^{2 x}
d /           2*x\
--\(5 - 3*x)*e   /
dx                
ddx(53x)e2x\frac{d}{d x} \left(5 - 3 x\right) e^{2 x}
Detail solution
  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\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(x)=53xf{\left(x \right)} = 5 - 3 x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate 53x5 - 3 x term by term:

      1. The derivative of the constant 55 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: xx goes to 11

          So, the result is: 33

        So, the result is: 3-3

      The result is: 3-3

    g(x)=e2xg{\left(x \right)} = e^{2 x}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    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}

    The result is: 2(53x)e2x3e2x2 \cdot \left(5 - 3 x\right) e^{2 x} - 3 e^{2 x}

  2. Now simplify:

    (76x)e2x\left(7 - 6 x\right) e^{2 x}


The answer is:

(76x)e2x\left(7 - 6 x\right) e^{2 x}

The graph
02468-8-6-4-2-1010-5000000000025000000000
The first derivative [src]
     2*x                2*x
- 3*e    + 2*(5 - 3*x)*e   
2(53x)e2x3e2x2 \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(3x2)e2x- 4 \cdot \left(3 x - 2\right) e^{2 x}
The third derivative [src]
               2*x
-4*(-1 + 6*x)*e   
4(6x1)e2x- 4 \cdot \left(6 x - 1\right) e^{2 x}
The graph
Derivative of (5-3*x)*e^(2*x)