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^2ysin(1/x))

Lösung

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

Lösung

y (2 x sin (\frac{1}{x}) - cos (\frac{1}{x}))

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = sin (\frac{1}{x})

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

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

\frac{\partial}{\partial x} (sin (\frac{1}{x})) = - \frac{cos ( \frac{1}{x} )}{x ^{2}}

= y (2 x sin (\frac{1}{x}) + (- \frac{cos ( \frac{1}{x} )}{x ^{2}}) x^{2})

Vereinfache

y (2 x sin (\frac{1}{x}) + (- \frac{cos ( \frac{1}{x} )}{x ^{2}}) x^{2}) : y (2 x sin (\frac{1}{x}) - cos (\frac{1}{x}))

= y (2 x sin (\frac{1}{x}) - cos (\frac{1}{x}))

Beliebte Beispiele

limit as x approaches 0 of-x^3

x \to 0 lim (- x^{3})

derivative f(x)=sqrt(x^2+6)

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

integral of 1/(y-yln(y))

\int \frac{1}{y - y ln ( y )} d y

f(x)=ln(sin(x)+4)

f (x) = ln (sin (x) + 4)

derivative of 1000(sin(x)(e^{-2x}))

\frac{d}{d x} (1000 (sin (x)) (e^{- 2 x}))