Matematička analiza → Diferencijalni račun → Izovdi složenih funkcija
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$y\text{'}=\frac{1}{g}·g\text{'}\phantom{\rule{0ex}{0ex}}$ $g\text{'}=\frac{{u}{\text{'}}{v}-{u}{v}{\text{'}}}{{{v}}^{2}}=\frac{{5}·{\left(}{4}{x}{-}{3}{\right)}-{5}{x}·{4}}{{\left(}{4}{x}{-}{3}{\right)}^{{2}}}=\frac{20x-15-20x}{{\left(4x-3\right)}^{2}}=\frac{-15}{{\left(4x-3\right)}^{2}}\phantom{\rule{0ex}{0ex}}$ $y\text{'}=\frac{1}{g}·g\text{'}=\frac{1}{\frac{5x}{4x-3}}·\frac{-15}{{\left(4x-3\right)}^{2}}\phantom{\rule{0ex}{0ex}}$ $y\text{'}=\frac{{4}{x}{-}{3}}{{5}x}·\frac{-{15}}{{\left(4x-3\right)}^{{2}}}\phantom{\rule{0ex}{0ex}}$ $y\text{'}=\frac{-3}{x·\left(4x-3\right)}\phantom{\rule{0ex}{0ex}}$
$y\text{'}=\frac{-3}{x·\left(4x-3\right)}$

$\frac{d}{dx}\left[f\left(g\left(x\right)\right)\right]=\frac{df}{dg}·\frac{dg}{dx}=f{\text{'}}_{g}·g{\text{'}}_{x}$

$\frac{d}{dx}\left(\mathrm{ln}x\right)=\frac{1}{x}$

${\left(\frac{u}{v}\right)}^{\text{'}}=\frac{u\text{'}·v-u·v\text{'}}{{v}^{2}}$