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^2+3sqrt(4-x^2))

Lösung

\frac{d}{d x} ((x^{2} + 3) 4 - x^{2})

Lösung

\frac{- 3 x ^{3} + 5 x}{4 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 3) 4 - x^{2})

Wende die Produktregel an:

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

f = x^{2} + 3, g = 4 - x^{2}

= \frac{d}{d x} (x^{2} + 3) 4 - x^{2} + \frac{d}{d x} (4 - x^{2}) (x^{2} + 3)

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

\frac{d}{d x} (4 - x^{2}) = - \frac{x}{4 - x ^{2}}

= 2 x 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) (x^{2} + 3)

Vereinfache

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

= \frac{- 3 x ^{3} + 5 x}{4 - x ^{2}}

Graph

Beliebte Beispiele

(cos^{3} (t))^{^{'}}

derivative of sin(1000x)

\frac{d}{d x} (sin (1000 x))

integral of 3/(2x^2+x-10)

\int \frac{3}{2 x ^{2} + x - 10} d x

integral of x(x^2+1)^6

\int x (x^{2} + 1)^{6} d x

(\partial)/(\partial x)((86)/(2+x^2+y^2))

\frac{\partial}{\partial x} (\frac{86}{2 + x ^{2} + y ^{2}})