(\partial)/(\partial w)(ln(2w^3-7y+3xy^2))

Lösung

\frac{\partial}{\partial w} (ln (2 w^{3} - 7 y + 3 x y^{2}))

\frac{6 w ^{2}}{2 w ^{3} - 7 y + 3 y ^{2} x}

Schritte zur Lösung

\frac{\partial}{\partial w} (ln (2 w^{3} - 7 y + 3 x y^{2}))

Behandle

y, x

als Konstanten

Wende die Kettenregel an:

\frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} \frac{\partial}{\partial w} (2 w^{3} - 7 y + 3 x y^{2})

= \frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} \frac{\partial}{\partial w} (2 w^{3} - 7 y + 3 x y^{2})

\frac{\partial}{\partial w} (2 w^{3} - 7 y + 3 x y^{2}) = 6 w^{2}

= \frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} \cdot 6 w^{2}

Vereinfache

\frac{1}{2 w ^{3} - 7 y + 3 x y ^{2}} \cdot 6 w^{2} : \frac{6 w ^{2}}{2 w ^{3} - 7 y + 3 y ^{2} x}

= \frac{6 w ^{2}}{2 w ^{3} - 7 y + 3 y ^{2} x}

p a r i t y f (x) = cot^{3} (sin (x))

x \to 0 lim (\frac{tan ( 3 x )}{sin ( 7 x )})

\frac{\partial}{\partial y} (z^{3} - x y + yz + y^{3} - 2)

\int \frac{- 11 x}{( x ^{2} + 5 ) ^{2}} d x

\int \frac{1}{s ^{2} + 3 s + 6} d s