(\partial)/(\partial x)(3y^2+20x^2y^3)

Lösung

\frac{\partial}{\partial x} (3 y^{2} + 20 x^{2} y^{3})

40 y^{3} x

Schritte zur Lösung

\frac{\partial}{\partial x} (3 y^{2} + 20 x^{2} y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3 y^{2}) + \frac{\partial}{\partial x} (20 x^{2} y^{3})

\frac{\partial}{\partial x} (3 y^{2}) = 0

\frac{\partial}{\partial x} (20 x^{2} y^{3}) = 40 y^{3} x

= 0 + 40 y^{3} x

Vereinfache

= 40 y^{3} x

l a pl a ce t r an s f or m cos^{2} (π t)

f^{^{'}} (x) = \frac{9}{2 9 x - 5}

\int 4 x - 3 d x

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

\frac{d y}{d t} - 2 t y = - 12 t^{2} e^{t^{2}}, y (0) = - 1