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

Derivative of 3^(2*x)

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

The graph:

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Piecewise:

The solution

You have entered [src] 
 2*x
3
32x3^{2 x} 
3^(2*x)
Detail solution

  1. Let u=2xu = 2 x.

  2. ddu3u=3ulog⁡(3)\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}

  3. Then, apply the chain rule. Multiply by ddx2x\frac{d}{d x} 2 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: 22

    The result of the chain rule is:

    2⋅32xlog⁡(3)2 \cdot 3^{2 x} \log{\left(3 \right)}

  4. Now simplify:

    2⋅9xlog⁡(3)2 \cdot 9^{x} \log{\left(3 \right)}

The answer is:

2⋅9xlog⁡(3)2 \cdot 9^{x} \log{\left(3 \right)}

The graph
02468-8-6-4-2-1010010000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   2*x       
2*3   *log(3)
2⋅32xlog⁡(3)2 \cdot 3^{2 x} \log{\left(3 \right)}
Simplify
The second derivative [src] 
   2*x    2   
4*3   *log (3)
4⋅32xlog⁡(3)24 \cdot 3^{2 x} \log{\left(3 \right)}^{2}
Simplify
The third derivative [src] 
   2*x    3   
8*3   *log (3)
8⋅32xlog⁡(3)38 \cdot 3^{2 x} \log{\left(3 \right)}^{3}
Simplify
The graph
Derivative of 3^(2*x)
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