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

Lösung

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

- y^{4} cos (y^{2} x)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

cos (x y^{2}) \frac{\partial}{\partial x} (x y^{2})

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

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

= - y^{2} cos (x y^{2}) y^{2}

Vereinfache

- y^{2} cos (x y^{2}) y^{2} : - y^{4} cos (y^{2} x)

= - y^{4} cos (y^{2} x)

\int \frac{3}{3 sin ( x ) - 4 cos ( x )} d x

d er i v a t i v e \frac{1}{cot ( \frac{1}{t} )}

\frac{d}{d x} (3^{c o s (2 x)})

x \to 3 lim (\frac{10}{x ^{2}})

\int_{0}^{4} (\frac{5 x}{x ^{2} + 9}) d x