Mister Exam

Derivative of ex^2

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 / 2\
 \x /
E    
$$e^{x^{2}}$$
E^(x^2)
Detail solution
  1. Let .

  2. The derivative of is itself.

  3. Then, apply the chain rule. Multiply by :

    1. Apply the power rule: goes to

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
     / 2\
     \x /
2*x*e    
$$2 x e^{x^{2}}$$
The second derivative [src]
              / 2\
  /       2\  \x /
2*\1 + 2*x /*e    
$$2 \left(2 x^{2} + 1\right) e^{x^{2}}$$
The third derivative [src]
                / 2\
    /       2\  \x /
4*x*\3 + 2*x /*e    
$$4 x \left(2 x^{2} + 3\right) e^{x^{2}}$$
The graph
Derivative of ex^2