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Derivative of:
Derivative of 2*x^5
Derivative of y=(x^3-3)(x^2+4x+1)
Derivative of y=12x+√x
Derivative of x*e^x+11
Identical expressions
a*e^(two *x)
a multiply by e to the power of (2 multiply by x)
a multiply by e to the power of (two multiply by x)
a*e(2*x)
a*e2*x
ae^(2x)
ae(2x)
ae2x
ae^2x

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

Derivative of ae^(2x)

The solution

You have entered [src]

   2*x
a*e

$$a e^{2 x}$$

d /   2*x\
--\a*e   /
dx

$$\frac{\partial}{\partial x} a e^{2 x}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 2 x$ .
2. The derivative of $e^{u}$ is itself.
3. 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:
  
  $2 e^{2 x}$
So, the result is: $2 a e^{2 x}$

The answer is:

$2 a e^{2 x}$

The first derivative [src]

     2*x
2*a*e

$$2 a e^{2 x}$$

Simplify

The second derivative [src]

     2*x
4*a*e

$$4 a e^{2 x}$$

Simplify

The third derivative [src]

     2*x
8*a*e

$$8 a e^{2 x}$$

Simplify