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

Question

1367 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-17T00:09:55

Please see below.

For $a > 0$ $a > 0$ , $\frac{d}{d x} (a^{x}) = a^{x} ln a$ $d/dx(a^x) = a^x lna$

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

$\frac{d}{d x} (a^{u}) = a^{u} ln (a) \frac{d u}{d x}$ $d/dx(a^u) = a^u ln(a) (du)/dx$

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−x2f(x)=2^(-x^2)?