(\partial)/(\partial x)(8+e^{-xy}cos(y))

Lösung

\frac{\partial}{\partial x} (8 + e^{- x y} cos (y))

- e^{- x y} y cos (y)

Schritte zur Lösung

\frac{\partial}{\partial x} (8 + e^{- x y} cos (y))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (8) + \frac{\partial}{\partial x} (e^{- x y} cos (y))

\frac{\partial}{\partial x} (8) = 0

\frac{\partial}{\partial x} (e^{- x y} cos (y)) = - y e^{- y x} cos (y)

= 0 - y e^{- y x} cos (y)

Vereinfache

= - e^{- x y} y cos (y)

t an g e n t f (x) = \frac{1}{2 + 3 x}, (2, \frac{1}{8})

d er i v a t i v e g (x) = (x^{2} + 1)^{3} (x^{2} + 2)^{6}

in v erse l a pl a ce \frac{s + 3}{s ^{2} + 2 s + 1}

d er i v a t i v e f (x) = 4 x^{4} - \frac{1}{4 x ^{4}}

\int (x + 4) (2 x + 1) d x