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(x-4)*e^(2*x-1)

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Derivative of:
Derivative of e^x/x^2
Derivative of 5x^3
Derivative of 5*x^2-2/sqrt(x)+sin(pi/4)
Derivative of 2^x+1
Identical expressions
(x- four)*e^(two *x- one)
(x minus 4) multiply by e to the power of (2 multiply by x minus 1)
(x minus four) multiply by e to the power of (two multiply by x minus one)
(x-4)*e(2*x-1)
x-4*e2*x-1
(x-4)e^(2x-1)
(x-4)e(2x-1)
x-4e2x-1
x-4e^2x-1
Similar expressions
(x-4)*e^(2*x+1)
(x+4)*e^(2*x-1)

The derivative of the function/ (x-4)*e^(2*x-1)

Derivative of (x-4)e^(2x-1)

The solution

You have entered [src]

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

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

d /         2*x - 1\
--\(x - 4)*e       /
dx

$$\frac{d}{d x} \left(x - 4\right) e^{2 x - 1}$$

Transform

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x - 4$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x - 4$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $\left(-1\right) 4$ is zero.
  The result is: $1$
$g{\left(x \right)} = e^{2 x - 1}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = 2 x - 1$ .
2. The derivative of $e^{u}$ is itself.
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - 1\right)$ :
  1. Differentiate $2 x - 1$ term by term:
    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: $2$
    2. The derivative of the constant $\left(-1\right) 1$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $2 e^{2 x - 1}$
The result is: $2 \left(x - 4\right) e^{2 x - 1} + e^{2 x - 1}$
Now simplify:

$\left(2 x - 7\right) e^{2 x - 1}$

The answer is:

$\left(2 x - 7\right) e^{2 x - 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

            -1 + 2*x
4*(-3 + x)*e

$$4 \left(x - 3\right) e^{2 x - 1}$$

Simplify

The third derivative [src]

              -1 + 2*x
4*(-5 + 2*x)*e

$$4 \cdot \left(2 x - 5\right) e^{2 x - 1}$$

Simplify

The graph

Derivative of (x-4)*e^(2*x-1)