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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

integral of (6x^3)/(sqrt(x^2+9))

\int \frac{6 x ^{3}}{x ^{2} + 9} d x

limit as t approaches-1 of t^2-1

t \to - 1 lim (t^{2} - 1)

integral of sin(5x)*cos(2x)

\int sin (5 x) \cdot cos (2 x) d x

derivative f(t)=ln(t^9+5)

d er i v a t i v e f (t) = ln (t^{9} + 5)

tangent y=4x-x^2,(1,3)

t an g e n t y = 4 x - x^{2}, (1, 3)