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Beliebt Rechnen >

(\partial)/(\partial x)(3x^2y^2+x/y)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (3 x^{2} y^{2}) = 6 y^{2} x

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

= 6 y^{2} x + \frac{1}{y}

Beliebte Beispiele

derivative y=sin(3x+2y)

d er i v a t i v e y = sin (3 x + 2 y)

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

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

derivative of 1/(5-x)

\frac{d}{d x} (\frac{1}{5 - x})

tangent f(x)=e^{-2x},(0,1)

t an g e n t f (x) = e^{- 2 x}, (0, 1)

y^{''}-2y^'+10y=e^{-x}

y^{^{''}} - 2 y^{^{'}} + 10 y = e^{- x}