(\partial)/(\partial x)(x^4-8xy-5y^2)

Lösung

\frac{\partial}{\partial x} (x^{4} - 8 x y - 5 y^{2})

4 x^{3} - 8 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{4} - 8 x y - 5 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{4}) - \frac{\partial}{\partial x} (8 x y) - \frac{\partial}{\partial x} (5 y^{2})

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

\frac{\partial}{\partial x} (8 x y) = 8 y

\frac{\partial}{\partial x} (5 y^{2}) = 0

= 4 x^{3} - 8 y - 0

Vereinfache

= 4 x^{3} - 8 y

\int \frac{5}{4 x ^{2}} d x

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

x \to 2 lim (\frac{11 x}{4 - x ^{2}})

d er i v a t i v e (3 x - 5) (x^{2} + 4)

\int \frac{7 x + 14}{x ^{2} + 5 x - 6} d x