(\partial)/(\partial y)(x^2-y^3+5x+12y+1)

Lösung

\frac{\partial}{\partial y} (x^{2} - y^{3} + 5 x + 12 y + 1)

- 3 y^{2} + 12

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2} - y^{3} + 5 x + 12 y + 1)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{2}) - \frac{\partial}{\partial y} (y^{3}) + \frac{\partial}{\partial y} (5 x) + \frac{\partial}{\partial y} (12 y) + \frac{\partial}{\partial y} (1)

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

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

\frac{\partial}{\partial y} (5 x) = 0

\frac{\partial}{\partial y} (12 y) = 12

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

= 0 - 3 y^{2} + 0 + 12 + 0

Vereinfache

= - 3 y^{2} + 12

d er i v a t i v e 2 x^{2} + 3

\int (e^{7 x}) d x

x \to 0 + lim (2 x)

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

k = 1 \sum \infty (- 1)^{k}