de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial t)(x^2ycos(z/t))

Lösung

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

Lösung

\frac{x ^{2} yz sin ( \frac{z}{t} )}{t ^{2}}

Schritte zur Lösung

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

Behandle

x, y, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

- sin (\frac{z}{t}) \frac{\partial}{\partial t} (\frac{z}{t})

= - sin (\frac{z}{t}) \frac{\partial}{\partial t} (\frac{z}{t})

\frac{\partial}{\partial t} (\frac{z}{t}) = - \frac{z}{t ^{2}}

= x^{2} y (- sin (\frac{z}{t}) (- \frac{z}{t ^{2}}))

Vereinfache

x^{2} y (- sin (\frac{z}{t}) (- \frac{z}{t ^{2}})) : \frac{x ^{2} yz sin ( \frac{z}{t} )}{t ^{2}}

= \frac{x ^{2} yz sin ( \frac{z}{t} )}{t ^{2}}

Beliebte Beispiele

derivative f(x)=-(13)/(x^6)

d er i v a t i v e f (x) = - \frac{13}{x ^{6}}

integral of 3/(tsqrt(t^2-1))

\int \frac{3}{t t ^{2} - 1} d t

limit as x approaches+0 of x/(x-1)

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

derivative f(x)=log_{10}(x^8+9)

d er i v a t i v e f (x) = lo g_{10} (x^{8} + 9)

derivative e^{sin(x)}

d er i v a t i v e e^{s i n (x)}