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Beliebt Rechnen >

derivative of (4x^3-7x+8/x)

Lösung

\frac{d}{d x} (\frac{4 x ^{3} - 7 x + 8}{x})

Lösung

\frac{8 x ^{3} - 8}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{3} - 7 x + 8}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x ^{3} - 7 x + 8 ) x - \frac{d x}{d x} ( 4 x ^{3} - 7 x + 8 )}{x ^{2}}

\frac{d}{d x} (4 x^{3} - 7 x + 8) = 12 x^{2} - 7

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

= \frac{( 12 x ^{2} - 7 ) x - 1 \cdot ( 4 x ^{3} - 7 x + 8 )}{x ^{2}}

Vereinfache

\frac{( 12 x ^{2} - 7 ) x - 1 \cdot ( 4 x ^{3} - 7 x + 8 )}{x ^{2}} : \frac{8 x ^{3} - 8}{x ^{2}}

= \frac{8 x ^{3} - 8}{x ^{2}}

Graph

Beliebte Beispiele

(dy)/(dx)=(1+3x^2)/((1+y)^2),y(1)=2

\frac{d y}{d x} = \frac{1 + 3 x ^{2}}{( 1 + y ) ^{2}}, y (1) = 2

integral of (4x+3)/(2x+1)

\int \frac{4 x + 3}{2 x + 1} d x

integral of r^{-2}

\int r^{- 2} d r

integral of x^2+2x-3

\int x^{2} + 2 x - 3 d x

integral of sqrt((x^2+4))

\int (x^{2} + 4) d x