de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

2 x + y^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

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

Vereinfache

= 2 x + y^{2}

Beliebte Beispiele

f (t) = 3 sin (2 t)

integral of x^2-5x+6

\int x^{2} - 5 x + 6 d x

(\partial)/(\partial x)(x^{1/4}y^{3/4})

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{3}{4}})

derivative cos(a^5+x^5)

d er i v a t i v e cos (a^{5} + x^{5})

integral of x/(sqrt(x^2+16))

\int \frac{x}{x ^{2} + 16} d x