(\partial)/(\partial x)(-6x^3+y^2+5xy)

Lösung

\frac{\partial}{\partial x} (- 6 x^{3} + y^{2} + 5 x y)

5 y - 18 x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (- 6 x^{3} + y^{2} + 5 x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= - \frac{\partial}{\partial x} (6 x^{3}) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (5 x y)

\frac{\partial}{\partial x} (6 x^{3}) = 18 x^{2}

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

\frac{\partial}{\partial x} (5 x y) = 5 y

= - 18 x^{2} + 0 + 5 y

Vereinfache

= 5 y - 18 x^{2}

s im pl i f y \frac{- 2 x}{( x ^{2} + 1 ) ^{2}}

d er i v a t i v e \frac{1}{x} + e^{x}

x \to - 6 lim (\frac{x + 9}{x + 6})

t an g e n t f (x) = 110 x - 16 x^{2}, at x = 0

in v erse l a pl a ce \frac{s \cdot ( s + 3 )}{s + 2}