(\partial)/(\partial x)(3x^3-9x+9xy^2)

Lösung

\frac{\partial}{\partial x} (3 x^{3} - 9 x + 9 x y^{2})

9 x^{2} - 9 + 9 y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x^{3} - 9 x + 9 x y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3 x^{3}) - \frac{\partial}{\partial x} (9 x) + \frac{\partial}{\partial x} (9 x y^{2})

\frac{\partial}{\partial x} (3 x^{3}) = 9 x^{2}

\frac{\partial}{\partial x} (9 x) = 9

\frac{\partial}{\partial x} (9 x y^{2}) = 9 y^{2}

= 9 x^{2} - 9 + 9 y^{2}

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{3}}}}{x ^{4}} d x

n or ma l y = (3 x^{2} + 1)^{2}, (0, 1)

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

d er i v a t i v e f (x) = 2 x^{2} - 1

x \to 0 + lim ((1 + x^{2})^{\frac{1}{x}})