(\partial)/(\partial x)(3x^2+2xy^2+1)

Lösung

\frac{\partial}{\partial x} (3 x^{2} + 2 x y^{2} + 1)

6 x + 2 y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x^{2} + 2 x y^{2} + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (2 x y^{2}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

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

\frac{\partial}{\partial x} (1) = 0

= 6 x + 2 y^{2} + 0

Vereinfache

= 6 x + 2 y^{2}

n = 1 \sum \infty \frac{5}{π ^{2}}

t an g e n t f (x) = \frac{3}{x}, (7, \frac{3}{7})

t an g e n t y = \frac{2}{1 + x ^{2}}, (2, 0.4)

x y^{^{'}} - y + x y^{4} = 0

ma c l a u r in \frac{x}{2 x + 1}