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Beliebt Rechnen >

derivative of (x-9xsqrt(x)/(sqrt(x)))

Lösung

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

Lösung

\frac{1 - 9 x}{2 x} - \frac{9}{2}

Schritte zur Lösung

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

Vereinfache

\frac{x - 9 x x}{x} : x (1 - 9 x)

= \frac{d}{d x} (x (1 - 9 x))

Wende die Produktregel an:

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

f = x, g = 1 - 9 x

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

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

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

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

Vereinfache

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

= \frac{1 - 9 x}{2 x} - \frac{9}{2}

Graph

Beliebte Beispiele

derivative f(x)= x/5

d er i v a t i v e f (x) = \frac{x}{5}

integral of y^4-8y^3+16y^2

\int y^{4} - 8 y^{3} + 16 y^{2} d y

(\partial)/(\partial y)(5e^y)

\frac{\partial}{\partial y} (5 e^{y})

derivative of tan^2(x^2)

\frac{d}{d x} (tan^{2} (x^{2}))

derivative of ((x+8)/(x^2))

\frac{d}{d x} (\frac{( x + 8 )}{x ^{2}})