(\partial)/(\partial y)(4x^2y^3-1)

Lösung

\frac{\partial}{\partial y} (4 x^{2} y^{3} - 1)

12 x^{2} y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (4 x^{2} y^{3} - 1)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (4 x^{2} y^{3}) - \frac{\partial}{\partial y} (1)

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

\frac{\partial}{\partial y} (1) = 0

= 12 x^{2} y^{2} - 0

Vereinfache

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

d er i v a t i v e 7 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\frac{d}{d x} (5 x^{3} y^{2} + x^{2} sin (y^{2}))

x \to 0 lim (- 10 x)

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

\int \frac{1}{2 x x} d x