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Derivative of:
Derivative of 4^(2*x)
Derivative of x^3-x+3
Derivative of x²-2
Derivative of sqrt(x)^2-2*x
Integral of d{x}:
4^(2*x)
Identical expressions
four ^(two *x)
4 to the power of (2 multiply by x)
four to the power of (two multiply by x)
4(2*x)
42*x
4^(2x)
4(2x)
42x
4^2x

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

Derivative of 4^(2*x)

The solution

You have entered [src]

 2*x
4

$$4^{2 x}$$

4^(2*x)

Detail solution

Let $u = 2 x$ .
$\frac{d}{d u} 4^{u} = 4^{u} \log{\left(4 \right)}$
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:

$2 \cdot 4^{2 x} \log{\left(4 \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2*x       
2*4   *log(4)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

   2*x    3   
8*4   *log (4)

$$8 \cdot 4^{2 x} \log{\left(4 \right)}^{3}$$

Simplify

The graph

Derivative of 4^(2*x)