How do you differentiate $f(x)=2^(-x^2)$ ?

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Answer 1 · 2017-08-17T00:09:55

Please see below.

For $a > 0$ , $d/dx(a^x) = a^x lna$

For exponent other then $x$ , we use the chain rule, so that

$d/dx(a^u) = a^u ln(a) (du)/dx$

So for this question, we have

$f'(x) = 2^(-x^2) ln(2) * (-2x)$

$= -2x2^(-x^2)ln(2)$

Or $-x2^(-x^2+1)ln(2)$

How do you differentiate f(x)=2^(-x^2)f(x)=2^(-x^2)?