(\partial)/(\partial x)(4x^3y+xy^2)

Lösung

\frac{\partial}{\partial x} (4 x^{3} y + x y^{2})

12 y x^{2} + y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{3} y + x y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x^{3} y) + \frac{\partial}{\partial x} (x y^{2})

\frac{\partial}{\partial x} (4 x^{3} y) = 12 y x^{2}

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

= 12 y x^{2} + y^{2}

d er i v a t i v e - \frac{2 x}{( 4 + x ^{2} ) ^{2}}

t an g e n t x^{3} - 6 x^{2} - 34 x + 40, at x = 4

\frac{\partial}{\partial z} (\frac{x y}{x + y + z})

\frac{d}{d x} (\frac{cos ( x )}{4 x})

x \to 1 - lim (x^{3} - 4)