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Identical expressions
e^x-e^(three *x)
e to the power of x minus e to the power of (3 multiply by x)
e to the power of x minus e to the power of (three multiply by x)
ex-e(3*x)
ex-e3*x
e^x-e^(3x)
ex-e(3x)
ex-e3x
e^x-e^3x
Similar expressions
e^x+e^(3*x)

The derivative of the function/ e^x-e^(3*x)

Derivative of e^x-e^(3*x)

The solution

You have entered [src]

 x    3*x
E  - E

$$e^{x} - e^{3 x}$$

E^x - E^(3*x)

Detail solution

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

The answer is:

$- 3 e^{3 x} + e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x      3*x
E  - 3*e

$$e^{x} - 3 e^{3 x}$$

Simplify

The second derivative [src]

/       2*x\  x
\1 - 9*e   /*e

$$\left(1 - 9 e^{2 x}\right) e^{x}$$

Simplify

The third derivative [src]

/        2*x\  x
\1 - 27*e   /*e

$$\left(1 - 27 e^{2 x}\right) e^{x}$$

Simplify

The graph

Derivative of e^x-e^(3*x)