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Derivative of:
Derivative of ln(1+x)
Derivative of e^sin(x)
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Derivative of e^(-2*x)
Identical expressions
(ye^y)+y^ two
(ye to the power of y) plus y squared
(ye to the power of y) plus y to the power of two
(yey)+y2
yey+y2
(ye^y)+y²
(ye to the power of y)+y to the power of 2
ye^y+y^2
Similar expressions
(ye^y)-y^2

The derivative of the function/ (ye^y)+y^2

Derivative of (ye^y)+y^2

The solution

You have entered [src]

   y    2
y*e  + y

$$y^{2} + y e^{y}$$

d /   y    2\
--\y*e  + y /
dy

$$\frac{d}{d y} \left(y^{2} + y e^{y}\right)$$

Transform

Detail solution

Differentiate $y^{2} + y e^{y}$ term by term:
1. Apply the product rule:
  
  $\frac{d}{d y} f{\left(y \right)} g{\left(y \right)} = f{\left(y \right)} \frac{d}{d y} g{\left(y \right)} + g{\left(y \right)} \frac{d}{d y} f{\left(y \right)}$
  
  $f{\left(y \right)} = y$ ; to find $\frac{d}{d y} f{\left(y \right)}$ :
  1. Apply the power rule: $y$ goes to $1$
  $g{\left(y \right)} = e^{y}$ ; to find $\frac{d}{d y} g{\left(y \right)}$ :
  1. The derivative of $e^{y}$ is itself.
  The result is: $y e^{y} + e^{y}$
2. Apply the power rule: $y^{2}$ goes to $2 y$
The result is: $y e^{y} + 2 y + e^{y}$
Now simplify:

$y e^{y} + 2 y + e^{y}$

The answer is:

$y e^{y} + 2 y + e^{y}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 y            y
e  + 2*y + y*e

$$y e^{y} + 2 y + e^{y}$$

Simplify

The second derivative [src]

       y      y
2 + 2*e  + y*e

$$y e^{y} + 2 e^{y} + 2$$

Simplify

The third derivative [src]

         y
(3 + y)*e

$$\left(y + 3\right) e^{y}$$

Simplify

The graph

Derivative of (ye^y)+y^2