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

Lösung

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

\frac{4 x}{x ^{2} + y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{2}) = 4 x (x^{2} + y^{2})

= \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 4 x (x^{2} + y^{2})

Vereinfache

\frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 4 x (x^{2} + y^{2}) : \frac{4 x}{x ^{2} + y ^{2}}

= \frac{4 x}{x ^{2} + y ^{2}}

d er i v a t i v e \frac{30}{( 1 - x ) ^{4}}

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

\int \frac{3}{5 x - 1} d x

\int (x^{2} - 7 x + 4) d x

\frac{d y}{d x} + \frac{y}{x} = e^{x}