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Beliebt Rechnen >

derivative of y^3+xy^2+y

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Beliebte Beispiele

derivative ((x+1)(x^2+1))/(x-2)

d er i v a t i v e \frac{( x + 1 ) ( x ^{2} + 1 )}{x - 2}

integral from-1 to 1 of (6x^5+3)

\int_{- 1}^{1} (6 x^{5} + 3) d x

derivative y=(9x)/(e^x)

d er i v a t i v e y = \frac{9 x}{e ^{x}}

f(x)=(x+1)/(x^2+1)

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

\frac{d y}{d x} - 3 y = 2