(\partial)/(\partial y)(y^6sin(4x))

Lösung

\frac{\partial}{\partial y} (y^{6} sin (4 x))

6 y^{5} sin (4 x)

Schritte zur Lösung

\frac{\partial}{\partial y} (y^{6} sin (4 x))

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= sin (4 x) \frac{\partial}{\partial y} (y^{6})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= sin (4 x) \cdot 6 y^{6 - 1}

Vereinfache

= 6 y^{5} sin (4 x)

\int_{0}^{1} 1 + x d x

\int_{0}^{1} π (1 - x^{2})^{2} d x

(3 + 4 x) + (5 y - 1) \frac{d y}{d x} = 0

t an g e n t f (x) = x^{2} + 5 x - 2, at x = 4

x \to 0 lim (2 x^{2} + 3 x)