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Beliebt Rechnen >

derivative of 1+x^2y^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (1) = 0

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

= 0 + 2 x y^{2} + 2 y \frac{d y}{d x} x^{2}

Vereinfache

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

Beliebte Beispiele

derivative y=(4x^6+7)^5

d er i v a t i v e y = (4 x^{6} + 7)^{5}

derivative 9x-6sqrt(x)

d er i v a t i v e 9 x - 6 x

(\partial)/(\partial x)(2cos(2x))

\frac{\partial}{\partial x} (2 cos (2 x))

derivative of cos^3(x/3)

\frac{d}{d x} (cos^{3} (\frac{x}{3}))

y^{''}-4y^'+21y=0

y^{^{''}} - 4 y^{^{'}} + 21 y = 0