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

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Derivative of:
Derivative of (x-2)^4
Derivative of (x-2)^2*(x-4)+5
Derivative of e^x*x^3
Derivative of 3*cos(x)
Identical expressions
(five - three *x)*e^(two *x)
(5 minus 3 multiply by x) multiply by e to the power of (2 multiply by x)
(five minus three multiply by x) multiply by e to the power of (two multiply by x)
(5-3*x)*e(2*x)
5-3*x*e2*x
(5-3x)e^(2x)
(5-3x)e(2x)
5-3xe2x
5-3xe^2x
Similar expressions
(5+3*x)*e^(2*x)

The derivative of the function/ (5-3*x)*e^(2*x)

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

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

$$\frac{d}{d x} \left(5 - 3 x\right) e^{2 x}$$

Transform

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = 5 - 3 x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $5 - 3 x$ term by term:
  1. The derivative of the constant $5$ 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: $x$ goes to $1$
      So, the result is: $3$
    So, the result is: $-3$
  The result is: $-3$
$g{\left(x \right)} = e^{2 x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = 2 x$ .
2. The derivative of $e^{u}$ is itself.
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $2$
  The result of the chain rule is:
  
  $2 e^{2 x}$
The result is: $2 \cdot \left(5 - 3 x\right) e^{2 x} - 3 e^{2 x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$2 \cdot \left(5 - 3 x\right) e^{2 x} - 3 e^{2 x}$$

Simplify

The second derivative [src]

               2*x
-4*(-2 + 3*x)*e

$$- 4 \cdot \left(3 x - 2\right) e^{2 x}$$

Simplify

The third derivative [src]

               2*x
-4*(-1 + 6*x)*e

$$- 4 \cdot \left(6 x - 1\right) e^{2 x}$$

Simplify

The graph

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