Question

Calcule as seguintes derivadas:
a) f(x)=x.lnx
b) f(x)=e^e^x
c) f(x)=ln^x4
d) f(x)=sen(cos(x))

Answer 1

$Ola'! \\ \\f(x)=x.ln(x) \\ f'(x)=x'ln(x)+x.\big(lng(x)\big)' \\ f'(x)=ln(x)+x. \frac{1}{x} \\ \boxed{f'(x)=ln(x)+1} \\ ------------------------------ \\ f(x)= e^{ e^{x} } \\ y= e^{ e^{x} } ~~por~log~temos: \\ ln(y)=ln \big(e^{ e^{x} }\big) \\ ln(y)= e^{x}ln(e) \\ ln(y)= e^{x} ~~--\ \textgreater \ derivando~temos: \\ \frac{y'}{y}= e^{x} \\ y'= e^{x}.y \\ y'= e^{x}. e^{ e^{x} } \\ \boxed{y'= e^{x+ e^{x} } } \\ ------------------------------- \\ a~c)~nao~entendi~quem~esta~no~expoente~se~e'~4~ou~x$
$------------------------------\\ f(x)=sen\big(cos(x)\big) \\ f'(x)=sen\big(cos(x)\big).con(x)' \\ f'(x)=sen\big(cos(x)\big)(-sen(x)) \\ \boxed{f'(x)=-sen(x)(cos(cos(x))}$