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Derivative of:
Derivative of 2*x/(x^2+4)
Derivative of sqrt(x)-1/(sqrt(x)*2-x-1)
Derivative of ln(x^2-4x)
Derivative of cos(pi/3-4*x)
Identical expressions
(two ^(x^ two))/ln2
(2 to the power of (x squared )) divide by ln2
(two to the power of (x to the power of two)) divide by ln2
(2(x2))/ln2
2x2/ln2
(2^(x²))/ln2
(2 to the power of (x to the power of 2))/ln2
2^x^2/ln2
(2^(x^2)) divide by ln2

The derivative of the function/ (2^(x^2))/ln2

Derivative of (2^(x^2))/ln2

The solution

You have entered [src]

 / 2\ 
 \x / 
2     
------
log(2)

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

2^(x^2)/log(2)

Detail solution

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

$2^{x^{2} + 1} x$

The answer is:

$2^{x^{2} + 1} x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     / 2\
     \x /
2*x*2

$$2 \cdot 2^{x^{2}} x$$

Simplify

The second derivative [src]

   / 2\                  
   \x / /       2       \
2*2    *\1 + 2*x *log(2)/

$$2 \cdot 2^{x^{2}} \left(2 x^{2} \log{\left(2 \right)} + 1\right)$$

Simplify

The third derivative [src]

     / 2\                         
     \x / /       2       \       
4*x*2    *\3 + 2*x *log(2)/*log(2)

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

Simplify