(\partial)/(\partial y)(ln(5+x^2y^2))

Lösung

\frac{\partial}{\partial y} (ln (5 + x^{2} y^{2}))

\frac{2 x ^{2} y}{5 + x ^{2} y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (ln (5 + x^{2} y^{2}))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{5 + x ^{2} y ^{2}} \frac{\partial}{\partial y} (5 + x^{2} y^{2})

= \frac{1}{5 + x ^{2} y ^{2}} \frac{\partial}{\partial y} (5 + x^{2} y^{2})

\frac{\partial}{\partial y} (5 + x^{2} y^{2}) = 2 x^{2} y

= \frac{1}{5 + x ^{2} y ^{2}} \cdot 2 x^{2} y

Vereinfache

\frac{1}{5 + x ^{2} y ^{2}} \cdot 2 x^{2} y : \frac{2 x ^{2} y}{5 + x ^{2} y ^{2}}

= \frac{2 x ^{2} y}{5 + x ^{2} y ^{2}}

t an g e n t f (x) = 4 x - x^{2}, at x = 2

s l o p e s = t^{3} - t^{2}

\frac{d}{d x} (16 x - x^{2})

t^{2} y^{^{''}} + 7 t y^{^{'}} + 9 y = 0

\int \frac{x ^{5}}{( x ^{3} + 1 ) ^{2}} d x