de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of x^3sqrt(5-x^2)

Lösung

\frac{d}{d x} (x^{3} 5 - x^{2})

Lösung

\frac{- 4 x ^{4} + 15 x ^{2}}{5 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x^{3} 5 - x^{2})

Wende die Produktregel an:

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

f = x^{3}, g = 5 - x^{2}

= \frac{d}{d x} (x^{3}) 5 - x^{2} + \frac{d}{d x} (5 - x^{2}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (5 - x^{2}) = - \frac{x}{5 - x ^{2}}

= 3 x^{2} 5 - x^{2} + (- \frac{x}{5 - x ^{2}}) x^{3}

Vereinfache

3 x^{2} 5 - x^{2} + (- \frac{x}{5 - x ^{2}}) x^{3} : \frac{- 4 x ^{4} + 15 x ^{2}}{5 - x ^{2}}

= \frac{- 4 x ^{4} + 15 x ^{2}}{5 - x ^{2}}

Graph

Beliebte Beispiele

implicit (dy)/(dx),x^2+y^2=25

im pl i c i t \frac{d y}{d x}, x^{2} + y^{2} = 25

(dx)/(dt)=4xt^5

\frac{d x}{d t} = 4 x t^{5}

derivative (x+2)/(x^3+x-6)

d er i v a t i v e \frac{x + 2}{x ^{3} + x - 6}

limit as x approaches 14 of sqrt(x+2)

x \to 14 lim (x + 2)

derivative g(x)=ln(xe^{-9x})

d er i v a t i v e g (x) = ln (x e^{- 9 x})