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Derivative of:
Derivative of 3^(2*x)
Derivative of (x-3)^4
Derivative of ln(1+x)
Derivative of ln(1-x)
Integral of d{x}:
3^(2*x)
Identical expressions
three ^(two *x)
3 to the power of (2 multiply by x)
three to the power of (two multiply by x)
3(2*x)
32*x
3^(2x)
3(2x)
32x
3^2x
Similar expressions
log3(3x)/3^2x-1
3^(2*x)/sin(2*x)

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

Derivative of 3^(2*x)

The solution

You have entered [src]

 2*x
3

$$3^{2 x}$$

3^(2*x)

Detail solution

Let $u = 2 x$ .
$\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}$
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:

$2 \cdot 3^{2 x} \log{\left(3 \right)}$
Now simplify:

$2 \cdot 9^{x} \log{\left(3 \right)}$

The answer is:

$2 \cdot 9^{x} \log{\left(3 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2*x       
2*3   *log(3)

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

Simplify

The second derivative [src]

   2*x    2   
4*3   *log (3)

$$4 \cdot 3^{2 x} \log{\left(3 \right)}^{2}$$

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of 3^(2*x)