(\partial)/(\partial x)(x^3e^y+cos(y))

Lösung

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

3 e^{y} x^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

\int_{1}^{e^{2}} x^{2} ln (x) d x

d er i v a t i v e \frac{x + 4}{x ^{3} + x - 5}

a re a y = 2 x, x = 5, y = \frac{2}{x}

\int \frac{x + 1}{x ^{3} + x ^{2} - 6 x} d x

t an g e n t y = x^{2}, at x = - 0.5