Resolva a derivada:
f(x)= Inx/x
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Boa tarde Ariely!
Solução!
Temos aqui uma derivada do produto.
![f(x)= \frac{lnx}{x}\\\\\\
f(x)=lnx. \frac{1}{x}\\\\\\\
u=lnx~~~~v= \xfrac{1}{x}\\\\\
u'= \frac{1}{x} ~~~~~~v'=- \frac{1}{ x^{2} }\\\\\\
Colocando ~~na~~ formula.\\\\\\\
\boxed{y'=u.v'+u'.v}](https://tex.z-dn.net/?f=f%28x%29%3D+%5Cfrac%7Blnx%7D%7Bx%7D%5C%5C%5C%5C%5C%5C%0Af%28x%29%3Dlnx.+%5Cfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%5C%5C%5C%0Au%3Dlnx%7E%7E%7E%7Ev%3D+%5Cxfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%5C%0Au%27%3D+%5Cfrac%7B1%7D%7Bx%7D+%7E%7E%7E%7E%7E%7Ev%27%3D-+%5Cfrac%7B1%7D%7B+x%5E%7B2%7D+%7D%5C%5C%5C%5C%5C%5C%0AColocando+%7E%7Ena%7E%7E+formula.%5C%5C%5C%5C%5C%5C%5C+%0A%5Cboxed%7By%27%3Du.v%27%2Bu%27.v%7D+++++%0A%0A+ "f(x)= \frac{lnx}{x}\\\\\\
f(x)=lnx. \frac{1}{x}\\\\\\\
u=lnx~~~~v= \xfrac{1}{x}\\\\\
u'= \frac{1}{x} ~~~~~~v'=- \frac{1}{ x^{2} }\\\\\\
Colocando ~~na~~ formula.\\\\\\\
\boxed{y'=u.v'+u'.v}")
![y'=u.v'+u'.v\\\\\\
y'=lnx.- \dfrac{1}{ x^{2} } + \dfrac{1}{x} . \dfrac{1}{x}\\\\\\\
y'=- \dfrac{lnx}{ x^{2} } + \dfrac{1}{ x^{2} } \\\\\\\
y'= \dfrac{ -lnx+1}{ x^{2} }\\\\\\\](https://tex.z-dn.net/?f=y%27%3Du.v%27%2Bu%27.v%5C%5C%5C%5C%5C%5C%0Ay%27%3Dlnx.-+%5Cdfrac%7B1%7D%7B+x%5E%7B2%7D+%7D+%2B+%5Cdfrac%7B1%7D%7Bx%7D+.+%5Cdfrac%7B1%7D%7Bx%7D%5C%5C%5C%5C%5C%5C%5C%0Ay%27%3D-+%5Cdfrac%7Blnx%7D%7B+x%5E%7B2%7D+%7D+%2B+%5Cdfrac%7B1%7D%7B+x%5E%7B2%7D+%7D+%5C%5C%5C%5C%5C%5C%5C%0Ay%27%3D+%5Cdfrac%7B+-lnx%2B1%7D%7B+x%5E%7B2%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0A+ "y'=u.v'+u'.v\\\\\\
y'=lnx.- \dfrac{1}{ x^{2} } + \dfrac{1}{x} . \dfrac{1}{x}\\\\\\\
y'=- \dfrac{lnx}{ x^{2} } + \dfrac{1}{ x^{2} } \\\\\\\
y'= \dfrac{ -lnx+1}{ x^{2} }\\\\\\\")
Boa tarde!
Bons estudos!
Solução!
Temos aqui uma derivada do produto.
Boa tarde!
Bons estudos!
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