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

Lösung

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

6 y^{2} sin (3 x y^{2} - y) cos (3 x y^{2} - y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= 2 sin (3 x y^{2} - y) cos (3 x y^{2} - y) \cdot 3 y^{2}

Vereinfache

= 6 y^{2} sin (3 x y^{2} - y) cos (3 x y^{2} - y)

im pl i c i t \frac{d y}{d x}, y = 1 1^{x}

\frac{d}{d x} ((x^{2} - 3) e^{x})

\int \frac{3 x ^{2} + 1}{x ^{5} - x} d x

s l o p e in t erce pt (0.5) (- 2.4)

y^{^{'}} = 5 y + y^{6}, y (0) = 1