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Derivative of:
Derivative of (x^3-1)(x^2+x+1)
Derivative of y/2
Derivative of (x+5)/(x-1)
Derivative of x+9
Integral of d{x}:
e^(2*x+1)
Identical expressions
e^(two *x+ one)
e to the power of (2 multiply by x plus 1)
e to the power of (two multiply by x plus one)
e(2*x+1)
e2*x+1
e^(2x+1)
e(2x+1)
e2x+1
e^2x+1
Similar expressions
e^(2*x-1)
ln(e^(2*x)+1)

The derivative of the function/ e^(2*x+1)

Derivative of e^(2*x+1)

The solution

You have entered [src]

 2*x + 1
E

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

E^(2*x + 1)

Detail solution

Let $u = 2 x + 1$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 1\right)$ :
1. Differentiate $2 x + 1$ term by term:
  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: $2$
  2. The derivative of the constant $1$ is zero.
  The result is: $2$
The result of the chain rule is:

$2 e^{2 x + 1}$
Now simplify:

$2 e^{2 x + 1}$

The answer is:

$2 e^{2 x + 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2*x + 1
2*e

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

Simplify

The second derivative [src]

   1 + 2*x
4*e

$$4 e^{2 x + 1}$$

Simplify

The third derivative [src]

   1 + 2*x
8*e

$$8 e^{2 x + 1}$$

Simplify

The graph

Derivative of e^(2*x+1)