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4^(2*x)
The derivative of the function/ 4^(2*x)

Derivative of 4^(2*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 2*x
4
42x4^{2 x} 
4^(2*x)
Detail solution

  1. Let u=2xu = 2 x.

  2. ddu4u=4ulog⁡(4)\frac{d}{d u} 4^{u} = 4^{u} \log{\left(4 \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⋅42xlog⁡(4)2 \cdot 4^{2 x} \log{\left(4 \right)}

  4. Now simplify:

    24x+2log⁡(2)2^{4 x + 2} \log{\left(2 \right)}

The answer is:

24x+2log⁡(2)2^{4 x + 2} \log{\left(2 \right)}

The graph
02468-8-6-4-2-101005000000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   2*x       
2*4   *log(4)
2⋅42xlog⁡(4)2 \cdot 4^{2 x} \log{\left(4 \right)}
Simplify
The second derivative [src] 
   2*x    2   
4*4   *log (4)
4⋅42xlog⁡(4)24 \cdot 4^{2 x} \log{\left(4 \right)}^{2}
Simplify
The third derivative [src] 
   2*x    3   
8*4   *log (4)
8⋅42xlog⁡(4)38 \cdot 4^{2 x} \log{\left(4 \right)}^{3}
Simplify
The graph
Derivative of 4^(2*x)
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