(\partial)/(\partial x)(2x^3+xy^2+5x^2+y^2)

Lösung

\frac{\partial}{\partial x} (2 x^{3} + x y^{2} + 5 x^{2} + y^{2})

6 x^{2} + 10 x + y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{3} + x y^{2} + 5 x^{2} + y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 x^{3}) + \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (5 x^{2}) + \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

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

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

\frac{\partial}{\partial x} (y^{2}) = 0

= 6 x^{2} + y^{2} + 10 x + 0

Vereinfache

= 6 x^{2} + 10 x + y^{2}

l a pl a ce t r an s f or m sin (4 t + 5 π)

\int \frac{x ^{2}}{2} y + \frac{x}{2} y^{2} cos (z) d z

\frac{\partial}{\partial u} (e^{u})

\int_{2}^{3} \frac{x}{x ^{2} + 4 x + 20} d x

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