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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

Beliebte Beispiele

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

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

integral of wsqrt(w^2-ln(3))

\int w w^{2} - ln (3) d w

limit as x approaches 0 of (3x)/(xe^x)

x \to 0 lim (\frac{3 x}{x e ^{x}})

integral of (3x^2-2x+5)/(x^2)

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

derivative f(x)=x^3sqrt(x)

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