(\partial)/(\partial x)(x^2cos(xy^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = cos (x y^{2})

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

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

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

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

Vereinfache

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

t \to + 0 lim (\frac{e ^{t} - 1}{t ^{9}})

\int 32 sin^{4} (2 x) d x

\frac{d}{d y} ((x^{2} + y^{2}) arctan (\frac{y}{x}))

\int \frac{x}{7} d x

y^{^{'}} - 5 y = 10 x