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Derivative of:
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Identical expressions
y=e^x^ two +x
y equally e to the power of x squared plus x
y equally e to the power of x to the power of two plus x
y=ex2+x
y=e^x²+x
y=e to the power of x to the power of 2+x
Similar expressions
y=e^x^2-x

The derivative of the function/ y=e^x^2+x

Derivative of y=e^x^2+x

The solution

You have entered [src]

 / 2\    
 \x /    
e     + x

$$x + e^{x^{2}}$$

  / / 2\    \
d | \x /    |
--\e     + x/
dx

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

Transform

Detail solution

Differentiate $x + e^{x^{2}}$ term by term:
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:
  
  $2 x e^{x^{2}}$
4. Apply the power rule: $x$ goes to $1$
The result is: $2 x e^{x^{2}} + 1$

The answer is:

$2 x e^{x^{2}} + 1$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$2 x e^{x^{2}} + 1$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of y=e^x^2+x