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

Lösung

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

2 x + 3 y^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

\frac{\partial}{\partial x} (2 y) = 0

= 2 x + 3 y^{2} + 0

Vereinfache

= 2 x + 3 y^{2}

y^{^{''}} + 4 y = 2 cos (2 t)

\int_{1}^{b} \frac{2 x}{x ^{2} + 4} d x

x^{2} y + y^{^{'}} = - 3 x^{2}

t an g e n t f (x) = 1 + 4 x, at x = 2

x \to c lim (x^{3} + 4 x^{2} - 3)