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Beliebt Rechnen >

derivative of (5x^3-7/x)

Lösung

\frac{d}{d x} (\frac{5 x ^{3} - 7}{x})

Lösung

\frac{10 x ^{3} + 7}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x ^{3} - 7}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 5 x ^{3} - 7 ) x - \frac{d x}{d x} ( 5 x ^{3} - 7 )}{x ^{2}}

\frac{d}{d x} (5 x^{3} - 7) = 15 x^{2}

\frac{d x}{d x} = 1

= \frac{15 x ^{2} x - 1 \cdot ( 5 x ^{3} - 7 )}{x ^{2}}

Vereinfache

\frac{15 x ^{2} x - 1 \cdot ( 5 x ^{3} - 7 )}{x ^{2}} : \frac{10 x ^{3} + 7}{x ^{2}}

= \frac{10 x ^{3} + 7}{x ^{2}}

Graph

Beliebte Beispiele

f(x)=10cos(30x-7)

integral of (-2x)/(1+x^2)

(\partial)/(\partial x)(e^{-8x})

d/(dy)(cos(2y))

limit as x approaches 0-of 5x^3-7x^2+2^x-2