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Derivative of:
Derivative of x^(1/2)
Derivative of x^(1/3)
Derivative of 1/sqrt(x)
Derivative of x*atan(x)
Integral of d{x}:
e^(4*x)
Equation:
e^(4*x)
Limit of the function:
e^(4*x)
Identical expressions
e^(four *x)
e to the power of (4 multiply by x)
e to the power of (four multiply by x)
e(4*x)
e4*x
e^(4x)
e(4x)
e4x
e^4x
Similar expressions
y=x^4+e^4x^2
3*sqrt(e^(4x+3))

The derivative of the function/ e^(4*x)

Derivative of e^(4*x)

The solution

You have entered [src]

 4*x
e

$$e^{4 x}$$

d / 4*x\
--\e   /
dx

$$\frac{d}{d x} e^{4 x}$$

Transform

Detail solution

Let $u = 4 x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} 4 x$ :
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: $4$
The result of the chain rule is:

$4 e^{4 x}$

The answer is:

$4 e^{4 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   4*x
4*e

$$4 e^{4 x}$$

Simplify

The second derivative [src]

    4*x
16*e

$$16 e^{4 x}$$

Simplify

The third derivative [src]

    4*x
64*e

$$64 e^{4 x}$$

Simplify

The graph

Derivative of e^(4*x)