de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of xy^4

Lösung

\frac{d}{d x} (x y^{4})

Lösung

y^{4} + 4 x y^{3} \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (x y^{4})

Wende die Produktregel an:

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

f = x, g = y^{4}

= \frac{d x}{d x} y^{4} + \frac{d}{d x} (y^{4}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (y^{4}) = 4 y^{3} \frac{d y}{d x}

= 1 \cdot y^{4} + 4 y^{3} \frac{d y}{d x} x

Vereinfache

= y^{4} + 4 x y^{3} \frac{d y}{d x}

Beliebte Beispiele

derivative of (x^2-9^3)

\frac{d}{d x} ((x^{2} - 9)^{3})

integral of x^{37}sin(x^{38})

\int x^{37} sin (x^{38}) d x

integral of sec(x/8)

\int sec (\frac{x}{8}) d x

integral from 8 to infinity of xe^{-5x}

\int_{8}^{\infty} x e^{- 5 x} d x

derivative of 12e^{x/2}

\frac{d}{d x} (12 e^{\frac{x}{2}})