Question 1082781
<pre>

There is no way to tell whether 2^x^2 means {{{matrix(2,1,"",2^((x^2)))}}} or {{{(2^x)^2}}}.

That's why it is necessary to use parentheses when typing algebra 
containing exponents or denominators all on one line.

If you mean the derivative of 

{{{matrix(2,1,"",y =2^((x^2)))}}}

We take natural logarithms of both sides

{{{matrix(2,1,"",ln(y) =ln(2^((x^2))))}}}

Then use a rule of logarithms:

{{{ln(y) =x^2*ln(2)}}}

[Note: ln(2) is just a constant.]

{{{"y'"/y=2x*ln(2)}}}

{{{"y'"=y*2x*ln(2)}}}

Replace y by {{{matrix(2,1,"",2^((x^2)))}}}

{{{matrix(2,1,"","y'"=2^((x^2))*2x*ln(2))}}}

{{{matrix(2,1,"","y'"=2^((x^2))*2^1*x*ln(2))}}}

Add exponents of 2

{{{matrix(2,1,"","y'"=2^((x^2+1))*x*ln(2))}}}


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If you mean the derivative of 

{{{y=(2^x)^2}}}

Multiply exponents:

{{{y=2^(2x)}}}

We take natural logarithms of both sides

{{{ln(y) =ln(2^(2x))}}}

Use a rule of logarithms:

{{{ln(y) =2x*ln(2)}}}

[Note: ln(2) is just a constant.  

{{{"y'"/y=2*ln(2)}}}

{{{"y'"=y*2*ln(2)}}}

Replace y by {{{2^(2x)}}}

{{{"y'"=2^(2x)*2*ln(2)}}}

{{{"y'"=2^(2x)*2^1*ln(2)}}}

Add exponents of 2

{{{"y'"=2^(2x+1)*ln(2)}}}

Edwin</pre>