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Derivative of:
Derivative of x^(4/5)
Derivative of x^3+2
Derivative of x^2-7*x
Derivative of ln(x)^2
Identical expressions
exp(three *x)+ three *exp(x)
exponent of (3 multiply by x) plus 3 multiply by exponent of (x)
exponent of (three multiply by x) plus three multiply by exponent of (x)
exp(3x)+3exp(x)
exp3x+3expx
Similar expressions
exp(3*x)-3*exp(x)

The derivative of the function/ exp(3*x)+3*exp(x)

Derivative of exp(3x)+3exp(x)

The solution

You have entered [src]

 3*x      x
e    + 3*e

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

exp(3*x) + 3*exp(x)

Detail solution

Differentiate $e^{3 x} + 3 e^{x}$ term by term:
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:
  
  $3 e^{3 x}$
4. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $e^{x}$ is itself.
  So, the result is: $3 e^{x}$
The result is: $3 e^{3 x} + 3 e^{x}$
Now simplify:

$3 \left(e^{2 x} + 1\right) e^{x}$

The answer is:

$3 \left(e^{2 x} + 1\right) e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x      3*x
3*e  + 3*e

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

Simplify

The second derivative [src]

  /       2*x\  x
3*\1 + 3*e   /*e

$$3 \left(3 e^{2 x} + 1\right) e^{x}$$

Simplify

The third derivative [src]

  /       2*x\  x
3*\1 + 9*e   /*e

$$3 \left(9 e^{2 x} + 1\right) e^{x}$$

Simplify