(\partial)/(\partial x)(x^3+xe^y-2y)

Lösung

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

3 x^{2} + e^{y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 3 x^{2} + e^{y} - 0

Vereinfache

= 3 x^{2} + e^{y}

\frac{d}{d x} (\frac{1}{( x + 2 ) ^{2}})

\int \frac{x ^{2}}{( x + 1 )} d x

\int 43 + 4 x d x

\frac{d}{d x} (- e^{x} cos (x))

t an g e n t f (x) = 2 7 x + 1, at x = 9