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Beliebt Rechnen >

derivative sqrt(x)(1-5sqrt(x))

Lösung

ableitung von

x (1 - 5 x)

Lösung

\frac{1 - 5 x}{2 x} - \frac{5}{2}

Schritte zur Lösung

\frac{d}{d x} (x (1 - 5 x))

Wende die Produktregel an:

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

f = x, g = 1 - 5 x

= \frac{d}{d x} (x) (1 - 5 x) + \frac{d}{d x} (1 - 5 x) x

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

\frac{d}{d x} (1 - 5 x) = - \frac{5}{2 x}

= \frac{1}{2 x} (1 - 5 x) + (- \frac{5}{2 x}) x

Vereinfache

\frac{1}{2 x} (1 - 5 x) + (- \frac{5}{2 x}) x : \frac{1 - 5 x}{2 x} - \frac{5}{2}

= \frac{1 - 5 x}{2 x} - \frac{5}{2}

Graph

Beliebte Beispiele

integral of 8/9 x^{-1/9}

\int \frac{8}{9} x^{- \frac{1}{9}} d x

limit as x approaches 3 of 3x

x \to 3 lim (3 x)

integral of 1/9 x^2

\int \frac{1}{9} x^{2} d x

derivative of (((4x^3+2x^2)/(sin(x)))^2)

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

fläche y=(-2x^2+3x-15)/(x^3-9x),x=1,x=2

a re a y = \frac{- 2 x ^{2} + 3 x - 15}{x ^{3} - 9 x}, x = 1, x = 2