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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(3x+2xy^2))

Lösung

\frac{\partial}{\partial x} (3 x + 2 x y^{2})

Lösung

\frac{3 + 2 y ^{2}}{2 3 x + 2 x y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x + 2 x y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 3 x + 2 x y ^{2}} \frac{\partial}{\partial x} (3 x + 2 x y^{2})

= \frac{1}{2 3 x + 2 x y ^{2}} \frac{\partial}{\partial x} (3 x + 2 x y^{2})

\frac{\partial}{\partial x} (3 x + 2 x y^{2}) = 3 + 2 y^{2}

= \frac{1}{2 3 x + 2 x y ^{2}} (3 + 2 y^{2})

Vereinfache

\frac{1}{2 3 x + 2 x y ^{2}} (3 + 2 y^{2}) : \frac{3 + 2 y ^{2}}{2 3 x + 2 x y ^{2}}

= \frac{3 + 2 y ^{2}}{2 3 x + 2 x y ^{2}}

Beliebte Beispiele

derivative y=arccos((11)/x)

d er i v a t i v e y = arccos (\frac{11}{x})

integral of xe^xy

\int x e^{x} y d x

integral from 1 to ln(x) of 1/t

\int_{1}^{l n (x)} \frac{1}{t} d t

integral of 1/(x^{2/3)}

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

tangent y=(x^2)/(x+3),(2, 4/5)

t an g e n t y = \frac{x ^{2}}{x + 3}, (2, \frac{4}{5})