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5^(2*x)
The derivative of the function/ 5^(2*x)

Derivative of 5^(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
5
52x5^{2 x} 
5^(2*x)
Detail solution

  1. Let u=2xu = 2 x.

  2. ddu5u=5ulog⁡(5)\frac{d}{d u} 5^{u} = 5^{u} \log{\left(5 \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⋅52xlog⁡(5)2 \cdot 5^{2 x} \log{\left(5 \right)}

  4. Now simplify:

    2⋅25xlog⁡(5)2 \cdot 25^{x} \log{\left(5 \right)}

The answer is:

2⋅25xlog⁡(5)2 \cdot 25^{x} \log{\left(5 \right)}

The graph
02468-8-6-4-2-10100500000000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   2*x       
2*5   *log(5)
2⋅52xlog⁡(5)2 \cdot 5^{2 x} \log{\left(5 \right)}
Simplify
The second derivative [src] 
   2*x    2   
4*5   *log (5)
4⋅52xlog⁡(5)24 \cdot 5^{2 x} \log{\left(5 \right)}^{2}
Simplify
The third derivative [src] 
   2*x    3   
8*5   *log (5)
8⋅52xlog⁡(5)38 \cdot 5^{2 x} \log{\left(5 \right)}^{3}
Simplify
The graph
Derivative of 5^(2*x)
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