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Beliebt Rechnen >

derivative of (5x-3(4x-3/x))

Lösung

\frac{d}{d x} ((5 x - 3) (4 x - \frac{3}{x}))

Lösung

40 x - \frac{9}{x ^{2}} - 12

Schritte zur Lösung

\frac{d}{d x} ((5 x - 3) (4 x - \frac{3}{x}))

Vereinfache

(5 x - 3) (4 x - \frac{3}{x}) : 20 x^{2} - 15 - 12 x + \frac{9}{x}

= \frac{d}{d x} (20 x^{2} - 15 - 12 x + \frac{9}{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (20 x^{2}) - \frac{d}{d x} (15) - \frac{d}{d x} (12 x) + \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (20 x^{2}) = 40 x

\frac{d}{d x} (15) = 0

\frac{d}{d x} (12 x) = 12

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

= 40 x - 0 - 12 - \frac{9}{x ^{2}}

Vereinfache

= 40 x - \frac{9}{x ^{2}} - 12

Graph

Beliebte Beispiele

integral of (x^2)/(x^3+9)

\int \frac{x ^{2}}{x ^{3} + 9} d x

derivative of 9x^2e^x

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

derivative of xsinh(x-cosh(x))

\frac{d}{d x} (x sinh (x) - cosh (x))

integral of (3x)/(x^2+5)

\int \frac{3 x}{x ^{2} + 5} d x

integral of csc^2(5x)

\int csc^{2} (5 x) d x