(\partial)/(\partial x)(5x^4+2xy+1)

Lösung

\frac{\partial}{\partial x} (5 x^{4} + 2 x y + 1)

20 x^{3} + 2 y

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x^{4} + 2 x y + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (5 x^{4}) + \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (5 x^{4}) = 20 x^{3}

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

\frac{\partial}{\partial x} (1) = 0

= 20 x^{3} + 2 y + 0

Vereinfache

= 20 x^{3} + 2 y

l a pl a ce t r an s f or m e^{2 t} cos (3 t)

\int + \frac{x ^{4} + 12 x ^{2} + 1}{x ^{5} + 20 x ^{3} + 5 x} d x

\int 2 e^{x} - 8 x d x

t an g e n t y = \frac{5}{1 + x ^{2}}, (4, 0.29412)

x \to \infty lim (2 x - 2 x)