Question

$Sa~se~calculeze~derivatele~functiilor~f:D \rightarrow R, ~unde~D~este \\ domeniul~de~\e{d}efini\e{t}ie:$
$a).f(x)= \sqrt{x^2-4x+3} ,~x \in (3,+ \infty) \\ b).f(x)= \sqrt{x^3+1} ,~x \in(0, + \infty)$

Answer 1

a) f'(x)=$= \frac{( x^{2} -4x+3)'}{2 \sqrt{ x^{2} -4x+3} }= \frac{2x-4}{2 \sqrt{ x^{2} -4x+3} }$, apoi se simplifica.
b) f'(x)=$\frac{(x^3+1)'}{2 \sqrt{x^3+1} } = \frac{3x^2}{2 \sqrt{x^3+1} } .$