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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial y} (2 k y - 5 x)

\int y^{- \frac{1}{3}} d y

\int \frac{5 x - 12}{x ^{3} - 6 x ^{2} + 8 x} d x

\int \frac{x - 3}{x ^{2} + 1} d x

t an g e n t \frac{7}{2 x + 1}, at a = 4