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y=(x^2-2x+3)e^x

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Identical expressions
y=(x^ two -2x+ three)e^x
y equally (x squared minus 2x plus 3)e to the power of x
y equally (x to the power of two minus 2x plus three)e to the power of x
y=(x2-2x+3)ex
y=x2-2x+3ex
y=(x²-2x+3)e^x
y=(x to the power of 2-2x+3)e to the power of x
y=x^2-2x+3e^x
Similar expressions
y=(x^2-2x-3)e^x
y=(x^2+2x+3)e^x

The derivative of the function/ y=(x^2-2x+3)e^x

Derivative of y=(x^2-2x+3)e^x

The solution

You have entered [src]

/ 2          \  x
\x  - 2*x + 3/*e

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

d // 2          \  x\
--\\x  - 2*x + 3/*e /
dx

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

Transform

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{2} - 2 x + 3$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} - 2 x + 3$ 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. 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: $2$
    So, the result is: $-2$
  3. The derivative of the constant $3$ is zero.
  The result is: $2 x - 2$
$g{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
The result is: $\left(2 x - 2\right) e^{x} + \left(x^{2} - 2 x + 3\right) e^{x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

/     2      \  x
\1 + x  + 2*x/*e

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

Simplify

The third derivative [src]

/     2      \  x
\3 + x  + 4*x/*e

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

Simplify

The graph

Derivative of y=(x^2-2x+3)e^x