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2^(3*x)

Derivative of 2^(3*x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 3*x
2   
23x2^{3 x}
d / 3*x\
--\2   /
dx      
ddx23x\frac{d}{d x} 2^{3 x}
Detail solution
  1. Let u=3xu = 3 x.

  2. ddu2u=2ulog(2)\frac{d}{d u} 2^{u} = 2^{u} \log{\left(2 \right)}

  3. Then, apply the chain rule. Multiply by ddx3x\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: xx goes to 11

      So, the result is: 33

    The result of the chain rule is:

    323xlog(2)3 \cdot 2^{3 x} \log{\left(2 \right)}

  4. Now simplify:

    38xlog(2)3 \cdot 8^{x} \log{\left(2 \right)}


The answer is:

38xlog(2)3 \cdot 8^{x} \log{\left(2 \right)}

The graph
02468-8-6-4-2-101002500000000
The first derivative [src]
   3*x       
3*2   *log(2)
323xlog(2)3 \cdot 2^{3 x} \log{\left(2 \right)}
The second derivative [src]
   3*x    2   
9*2   *log (2)
923xlog(2)29 \cdot 2^{3 x} \log{\left(2 \right)}^{2}
The third derivative [src]
    3*x    3   
27*2   *log (2)
2723xlog(2)327 \cdot 2^{3 x} \log{\left(2 \right)}^{3}
The graph
Derivative of 2^(3*x)