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Identical expressions
y=(x- one)e^x^ two
y equally (x minus 1)e to the power of x squared
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y=x-1ex2
y=(x-1)e^x²
y=(x-1)e to the power of x to the power of 2
y=x-1e^x^2
Similar expressions
y=(x+1)e^x^2

The derivative of the function/ y=(x-1)e^x^2

Derivative of y=(x-1)e^x^2

The solution

You have entered [src]

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

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

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

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

Transform

Detail solution

Apply the product rule:

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

                                        / 2\
  /       2                /       2\\  \x /
2*\3 + 6*x  + 2*x*(-1 + x)*\3 + 2*x //*e

$$2 \cdot \left(2 x \left(x - 1\right) \left(2 x^{2} + 3\right) + 6 x^{2} + 3\right) e^{x^{2}}$$

Simplify

The graph

Derivative of y=(x-1)e^x^2