(\partial)/(\partial x)(3x^4+5y^4+9xy)

Lösung

\frac{\partial}{\partial x} (3 x^{4} + 5 y^{4} + 9 x y)

12 x^{3} + 9 y

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x^{4} + 5 y^{4} + 9 x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3 x^{4}) + \frac{\partial}{\partial x} (5 y^{4}) + \frac{\partial}{\partial x} (9 x y)

\frac{\partial}{\partial x} (3 x^{4}) = 12 x^{3}

\frac{\partial}{\partial x} (5 y^{4}) = 0

\frac{\partial}{\partial x} (9 x y) = 9 y

= 12 x^{3} + 0 + 9 y

Vereinfache

= 12 x^{3} + 9 y

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{x}

\int \frac{8 x - 3}{12 x - 4 x ^{2} - 5} d x

\frac{d}{d X} (\frac{8 X ^{2} + 2 X + 8}{X})

l a pl a ce t r an s f or m \frac{t - 5}{5}

\int sin^{3} (11 x) d x