(\partial)/(\partial x)(x^2y^3+2xy^{-3}+5x+3y+11)

Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} + 2 x y^{- 3} + 5 x + 3 y + 11)

2 x y^{3} + \frac{2}{y ^{3}} + 5

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} + 2 x y^{- 3} + 5 x + 3 y + 11)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2} y^{3}) + \frac{\partial}{\partial x} (2 x y^{- 3}) + \frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (3 y) + \frac{\partial}{\partial x} (11)

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

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

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

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

\frac{\partial}{\partial x} (11) = 0

= 2 y^{3} x + \frac{2}{y ^{3}} + 5 + 0 + 0

Vereinfache

= 2 x y^{3} + \frac{2}{y ^{3}} + 5

t \to 5 lim (\frac{1}{t ^{2} - 4 t - 5} - \frac{1}{6 ( t - 5 )})

n = 0 \sum \infty \frac{x ^{n}}{n + 2}

x \to 0 lim (\frac{8}{1 + sin ( x )})

d er i v a t i v e \frac{lo g _{5} ( x )}{6 + x ^{5}}

\frac{\partial}{\partial x} (y cos (y - 2 x))