Question

f(x) = √1-sen(x) / √1-cos(x)
Derivar...
raiz em todo o termo.

Answer 1

$f(x)= \sqrt{1+sen(x)}/ \sqrt{1 - sen(x)}$
$f(x)= 1+sen(x)/ 1 - sen(x)$
$f(x)= ((1+senx)/ (1 - senx))^(1/2)$
$f(x)= (1/2). ((1+senx)/ (1 - senx))$
$f(x)= [((1+senx) - (1 - senx))]/2$
$f '(x)= [cosx/(1+senx) +cosx/(1-senx)]/2$
$f '(x)= [cosx(1-senx) + cosx(1+senx)]/2(1-sen ^{2} x)$
$f '(x)= [cosx-cosx.senx + cosx+cosx.senx]/2(1-sen ^{2} x)$
$f '(x)= [cosx + cosx]/2(1-sen ^{2} x)$
$f '(x)= [2cosx]/2cos ^{2} x$
$f '(x)= [cosx]/cos ^{2} x$
$f '(x)= 1/cosx$
$f '(x)= secx$