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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x^{2} y + y^{2})

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

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

\int (x^{8} + sec^{2} (x)) d x

d er i v a t i v e f (x) = \frac{( x ^{3} + 9 )}{x ^{3}}

x \to 0 lim (tan (3 x))

\int \frac{x - 2}{x} d x

d er i v a t i v e y = - 2 e^{- x^{2}} x