Question

$f(x)=2\sqrt{x}\cdot(lnx-1).$ Nu pot deriva singur...

Answer 1

Răspuns:

Explicație pas cu pas:

Se vor aplica formulele..

$(u*v)'=u'x-uv';~~~(\sqrt{x} )'=\frac{1}{2\sqrt{x} } ;~~~(lnx)'=\frac{1}{x};~~~(const)'=0.\\f'(x)=[2\sqrt{x} *(lnx-1)]'=2*[\sqrt{x} *(lnx-1)]'=2*[(\sqrt{x} )'*(lnx-1)+\sqrt{x}*(lnx-1)']=2*[\frac{1}{2\sqrt{x} }*(lnx-1)+\sqrt{x}*\frac{1}{x} ]=\frac{1}{\sqrt{x} }*(lnx-1)+\frac{2}{\sqrt{x} } =\frac{1}{\sqrt{x} } *(lnx-1+2)=\frac{1}{\sqrt{x} } *(lnx+1)=\frac{lnx+1}{\sqrt{x} } .$