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Derivative of:
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Identical expressions
two *x+e^(three *x)
2 multiply by x plus e to the power of (3 multiply by x)
two multiply by x plus e to the power of (three multiply by x)
2*x+e(3*x)
2*x+e3*x
2x+e^(3x)
2x+e(3x)
2x+e3x
2x+e^3x
Similar expressions
2*x-e^(3*x)

The derivative of the function/ 2*x+e^(3*x)

Derivative of 2x+e^(3x)

The solution

You have entered [src]

       3*x
2*x + e

$$e^{3 x} + 2 x$$

d /       3*x\
--\2*x + e   /
dx

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

Transform

Detail solution

Differentiate $2 x + e^{3 x}$ term by term:
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: $2$
2. Let $u = 3 x$ .
3. The derivative of $e^{u}$ is itself.
4. 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 result is: $3 e^{3 x} + 2$

The answer is:

$3 e^{3 x} + 2$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       3*x
2 + 3*e

$$3 e^{3 x} + 2$$

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

The graph

Derivative of 2*x+e^(3*x)