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Derivative of:
Derivative of x^x^x
Derivative of x^-6
Derivative of x^-11
Derivative of -x/2
Differential equation:
y'
Integral of d{x}:
e^(3x)
Graphing y =:
e^(3x)
Identical expressions
y'=e^(3x)
y stroke first (1st) order equally e to the power of (3x)
y'=e(3x)
y'=e3x
y'=e^3x
Similar expressions
А*e^(3x)x
e^3*x+e^x×x
e^(3*x)+2
(2+e^(3*x))/(9-e^(x*(-4)))

The derivative of the function/ y'=e^(3x)

Derivative of y'=e^(3x)

The solution

You have entered [src]

 3*x
e

$$e^{3 x}$$

d / 3*x\
--\e   /
dx

$$\frac{d}{d x} e^{3 x}$$

Transform

Detail solution

Let $u = 3 x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x$ :
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: $3$
The result of the chain rule is:

$3 e^{3 x}$

The answer is:

$3 e^{3 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3*x
3*e

$$3 e^{3 x}$$

Simplify

The second derivative [src]

   3*x
9*e

$$9 e^{3 x}$$

Simplify

The third derivative [src]

    3*x
27*e

$$27 e^{3 x}$$

Simplify

3-я производная [src]

    3*x
27*e

$$27 e^{3 x}$$

Simplify

The graph

Derivative of y'=e^(3x)