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)(pi*xsqrt(x^2+y^2))

Lösung

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

Lösung

\frac{π ( 2 x ^{2} + y ^{2} )}{x ^{2} + y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + y^{2}

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

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

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

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

Vereinfache

π (1 \cdot x^{2} + y^{2} + \frac{x}{x ^{2} + y ^{2}} x) : \frac{π ( 2 x ^{2} + y ^{2} )}{x ^{2} + y ^{2}}

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

Beliebte Beispiele

derivative of ln(1/(6+x))

\frac{d}{d x} (ln (\frac{1}{6 + x}))

limit as x approaches 3 of sqrt(x+1)

x \to 3 lim (x + 1)

integral of sech^2(x)

\int sech^{2} (x) d x

laplacetransform 1/2 (t-2)^2

l a pl a ce t r an s f or m \frac{1}{2} (t - 2)^{2}

(\partial)/(\partial x)(4y+xe^{x/y})

\frac{\partial}{\partial x} (4 y + x e^{\frac{x}{y}})