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Beliebt Rechnen >

derivative of 2xy^2+4

Lösung

\frac{d}{d x} (2 x y^{2} + 4)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (2 x y^{2} + 4)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x y^{2}) + \frac{d}{d x} (4)

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

\frac{d}{d x} (4) = 0

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

Vereinfache

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

Beliebte Beispiele

derivative of (1+3x^5)

\frac{d}{d x} ((1 + 3 x)^{5})

integral of 1/(X^2)

\int \frac{1}{X ^{2}} d X

integral of (5x^2-12)/((x^2-6x+13)^2)

\int \frac{5 x ^{2} - 12}{( x ^{2} - 6 x + 13 ) ^{2}} d x

integral of (4x)/(x^3-x^2-x+1)

\int \frac{4 x}{x ^{3} - x ^{2} - x + 1} d x

im pl i c i t y x = c