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Beliebt Rechnen >

(\partial)/(\partial y)(ln(1+x^2+y))

Lösung

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

Lösung

\frac{1}{1 + x ^{2} + y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

Beliebte Beispiele

integral of (18)/((x^2-1)^2)

\int \frac{18}{( x ^{2} - 1 ) ^{2}} d x

y^'+7x^{-1}y=x^2

y^{^{'}} + 7 x^{- 1} y = x^{2}

derivative 10arcsin(e^{x/2})

d er i v a t i v e 10 arcsin (e^{\frac{x}{2}})

integral of (4x^2)/(x^2+7)

\int \frac{4 x ^{2}}{x ^{2} + 7} d x

limit as x approaches 3 of 1/(x-2)

x \to 3 lim (\frac{1}{x - 2})