Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^(2*x)
Derivative of 5/x
Derivative of arcsin(5x)
Derivative of ln(x^2-9)
Integral of d{x}:
e^(2*x)
Equation:
e^(2*x)
Limit of the function:
e^(2*x)
Identical expressions
e^(two *x)
e to the power of (2 multiply by x)
e to the power of (two multiply by x)
e(2*x)
e2*x
e^(2x)
e(2x)
e2x
e^2x
Similar expressions
y=ln(e^2x+1)-2arctge^x
sqrt(x^1/3)*e^2x
2x*e^(2x)
1-e^(2x)-2xe^(2x)

The derivative of the function/ e^(2*x)

Derivative of e^(2*x)

The solution

You have entered [src]

 2*x
E

$$e^{2 x}$$

E^(2*x)

Detail solution

Let $u = 2 x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
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: $2$
The result of the chain rule is:

$2 e^{2 x}$

The answer is:

$2 e^{2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2*x
2*e

$$2 e^{2 x}$$

Simplify

The second derivative [src]

   2*x
4*e

$$4 e^{2 x}$$

Simplify

The third derivative [src]

   2*x
8*e

$$8 e^{2 x}$$

Simplify

The graph

Derivative of e^(2*x)