(\partial)/(\partial y)(x-y^3+y^2sin(x))

Lösung

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

- 3 y^{2} + 2 y sin (x)

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 0 - 3 y^{2} + 2 y sin (x)

Vereinfache

= - 3 y^{2} + 2 y sin (x)

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

\int_{- 2}^{2} - 3 x^{2} - 4 x d x

\int \frac{5}{x ^{2} + 3 x - 4} d x

\int (5 x - 3)^{4} d x

s l o p e y = \frac{x ^{2}}{3} + x + \frac{1}{2}