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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

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

Vereinfache

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

d er i v a t i v e f (x) = (6 x^{2} - 9 x) e^{x}

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

n = 1 \sum \infty (\frac{1}{6})^{n}

t an g e n t x^{2} + 8 x - 7

d er i v a t i v e \frac{9 x}{2 ^{x}}