de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of sqrt(x)(x-9^2)

Lösung

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

Lösung

\frac{5 x ^{2} - 54 x + 81}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = (x - 9)^{2}

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} (x - 9)^{2} + 2 (x - 9) x

Vereinfache

\frac{1}{2 x} (x - 9)^{2} + 2 (x - 9) x : \frac{5 x ^{2} - 54 x + 81}{2 x}

= \frac{5 x ^{2} - 54 x + 81}{2 x}

Graph

Beliebte Beispiele

integral of (4x+sqrt(x))

\int (4 x + x) d x

tangent y=sqrt(x),\at x= 1/4

t an g e n t y = x, at x = \frac{1}{4}

integral of (ln^5(x^2))/x

\int \frac{ln ^{5} ( x ^{2} )}{x} d x

derivative of-6x^2+6x

\frac{d}{d x} (- 6 x^{2} + 6 x)

integral of 2(3-e^{-t})

\int 2 (3 - e^{- t}) d t