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Derivative of:
Derivative of y=5
Derivative of x^6-6x^10+12x
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Derivative of e^((x^2)-x)
Identical expressions
e^((x^ two)-x)
e to the power of ((x squared ) minus x)
e to the power of ((x to the power of two) minus x)
e((x2)-x)
ex2-x
e^((x²)-x)
e to the power of ((x to the power of 2)-x)
e^x^2-x
Similar expressions
(e^x^2-x)/tg(1/x)
e^((x^2)+x)

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

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

The solution

You have entered [src]

  2    
 x  - x
E

$$e^{x^{2} - x}$$

E^(x^2 - x)

Detail solution

Let $u = x^{2} - x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - x\right)$ :
1. Differentiate $x^{2} - x$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. 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: $-1$
  The result is: $2 x - 1$
The result of the chain rule is:

$\left(2 x - 1\right) e^{x^{2} - x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

/              2\  x*(-1 + x)
\2 + (-1 + 2*x) /*e

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

Simplify

The third derivative [src]

           /              2\  x*(-1 + x)
(-1 + 2*x)*\6 + (-1 + 2*x) /*e

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

Simplify

The graph

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