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Derivative of:
Derivative of tanh(x)
Derivative of tanx
Derivative of tg2x
Derivative of 5^(2*x)
Integral of d{x}:
5^(2*x)
Identical expressions
five ^(two *x)
5 to the power of (2 multiply by x)
five to the power of (two multiply by x)
5(2*x)
52*x
5^(2x)
5(2x)
52x
5^2x

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

Derivative of 5^(2*x)

The solution

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 2*x
5

$$5^{2 x}$$

5^(2*x)

Detail solution

Let $u = 2 x$ .
$\frac{d}{d u} 5^{u} = 5^{u} \log{\left(5 \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $2$
The result of the chain rule is:

$2 \cdot 5^{2 x} \log{\left(5 \right)}$
Now simplify:

$2 \cdot 25^{x} \log{\left(5 \right)}$

The answer is:

$2 \cdot 25^{x} \log{\left(5 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2*x       
2*5   *log(5)

$$2 \cdot 5^{2 x} \log{\left(5 \right)}$$

Simplify

The second derivative [src]

   2*x    2   
4*5   *log (5)

$$4 \cdot 5^{2 x} \log{\left(5 \right)}^{2}$$

Simplify

The third derivative [src]

   2*x    3   
8*5   *log (5)

$$8 \cdot 5^{2 x} \log{\left(5 \right)}^{3}$$

Simplify

The graph

Derivative of 5^(2*x)