[m]x(o)=1[/m]
[m] Δx=0,03[/m]
[m]Δy=f(x_{o}+ Δx)-f(x_{o})[/m] ⇒
[m]f(x_{o}+ Δx)=f(x_{o})+ Δy[/m]
[m] Δy ≈ df[/m]
[m]df(x_{o})=f`(x_{o})\cdot Δx[/m]
[m]f(x_(o))=5^{\sqrt{1}}=5[/m]
[m]f`(x)=(5^{\sqrt{x}})`=5^{\sqrt{x}}\cdot ln5 \cdot (\sqrt{x})`=5^{\sqrt{x}}\cdot ln5 \cdot (\frac{1}{2\sqrt{x}})[/m]
[m]f`(1)=5^{\sqrt{1}}\cdot ln5 \cdot (\frac{1}{2\sqrt{1}})=2,5ln5[/m]
[m]5^{\sqrt{1,03}} ≈5+2,5ln5\cdot 0,03=[/m]