Title: Trigonometriset funktiot. Aste

Tiedetään, että \(f([value])=[value]\) ja \(f'([value])=[value]\). Määritä \(g'([value])\), kun \(g(x)=f(x)^[value]\)

\(g'([value])=\)
Feedback: \(g(x)=f(x)^[value]\) Derivoidaan \(g'(x)=[value]f(x)^[value]\cdot f'(x)\) Sijoitus \(f([value])=[value]\) ja \(f'([value])=[value]\) \(g'([value])=[value]\cdot[value]^[value]\cdot([value])=[value]\)

Olkoon \(f(x)=x^[value]([value]+x^[value])^[value]\)

Määritä

\(f'(1)=\)
Feedback: \(f(x)=x^[value]([value]+x^[value])^[value]\) Derivoidaan \(f'(x)=[value]x^[value]([value]+x^[value])^[value]+[value]([value]+x^[value])^[value][value]x^[value]x^[value]=[value]x^[value]([value]+x^[value])^[value]+[value]([value]+x^[value])^[value]x^[value]\) Sijoitus \(f'(1)=[value]\)

Olkoon \(f(x)=(x^[value]-[value])^[value]\)

Määritä derivaatan nollakohdista suurempi

\(x=\)
Feedback: \(f(x)=(x^[value]-[value])^[value]\) Derivoidaan \(f'(x)=[value](x^[value]-[value])^[value]\cdot[value]x^[value]\) Nollakohdat \([value](x^[value]-[value])^[value]\cdot[value]x^[value]=0\) Tulon nollasääntö \([value]x^[value]=0\) tai \([value](x^[value]-[value])^[value]=0\) \(x=0\) tai \(x^[value]-[value]=0\) \(x=[value]\)

Olkoon \(f(x)=(x^[value]-[value])^[value]\)

Määritä. Anna vastaus kahden merkitsevän numeron tarkkuudella.

\(f'([value])=\)
Feedback: \(f(x)=(x^[value]-[value])^[value]\) Derivoidaan \(f'(x)=[value](x^[value]-[value])^[value]\cdot[value]x^[value]\) Sijoitus \(f'([value])=[value](([value])^[value]-[value])^[value]\cdot[value]\cdot([value])^[value]=[value]\)

Laske lausekkeen \(sin(2\alpha)+2cos(\alpha)\) arvo kahden merkitsevän numeron tarkkuudella, kun \(\alpha=[value]°\).
Feedback: Sijoitus \(sin(2\cdot[value]°)+2cos([value]°)=[value]\)

Laske tarkka arvo

\(sin([value]°)=\)
Feedback: \(sin([value]°)=[value]\)

Laske tarkka arvo

\(cos([value]°)=\)
Feedback: \(cos([value]°)=[value]\)