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Derivative of:
Derivative of 2^(3*x)
Derivative of x^3*e^x
Derivative of x*e^(2*x)
Derivative of 9/x
Integral of d{x}:
2^(3*x)
Identical expressions
two ^(three *x)
2 to the power of (3 multiply by x)
two to the power of (three multiply by x)
2(3*x)
23*x
2^(3x)
2(3x)
23x
2^3x

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

Derivative of 2^(3*x)

The solution

You have entered [src]

 3*x
2

$$2^{3 x}$$

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

$$\frac{d}{d x} 2^{3 x}$$

Transform

Detail solution

Let $u = 3 x$ .
$\frac{d}{d u} 2^{u} = 2^{u} \log{\left(2 \right)}$
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:

$3 \cdot 2^{3 x} \log{\left(2 \right)}$
Now simplify:

$3 \cdot 8^{x} \log{\left(2 \right)}$

The answer is:

$3 \cdot 8^{x} \log{\left(2 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3*x       
3*2   *log(2)

$$3 \cdot 2^{3 x} \log{\left(2 \right)}$$

Simplify

The second derivative [src]

   3*x    2   
9*2   *log (2)

$$9 \cdot 2^{3 x} \log{\left(2 \right)}^{2}$$

Simplify

The third derivative [src]

    3*x    3   
27*2   *log (2)

$$27 \cdot 2^{3 x} \log{\left(2 \right)}^{3}$$

Simplify

The graph

Derivative of 2^(3*x)