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Beliebt Rechnen >

derivative of (x^2+14/(x^8))

Lösung

\frac{d}{d x} (\frac{x ^{2} + 14}{x ^{8}})

Lösung

\frac{2 ( - 3 x ^{2} - 56 )}{x ^{9}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 14}{x ^{8}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 14 ) x ^{8} - \frac{d}{d x} ( x ^{8} ) ( x ^{2} + 14 )}{( x ^{8} ) ^{2}}

\frac{d}{d x} (x^{2} + 14) = 2 x

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{2 x x ^{8} - 8 x ^{7} ( x ^{2} + 14 )}{( x ^{8} ) ^{2}}

Vereinfache

\frac{2 x x ^{8} - 8 x ^{7} ( x ^{2} + 14 )}{( x ^{8} ) ^{2}} : \frac{2 ( - 3 x ^{2} - 56 )}{x ^{9}}

= \frac{2 ( - 3 x ^{2} - 56 )}{x ^{9}}

Graph

Beliebte Beispiele

y^{''}+4y^'+6.25y=3.125(x+1)^2

y^{^{''}} + 4 y^{^{'}} + 6.25 y = 3.125 (x + 1)^{2}

y^{^{'}} = 2 x y^{- 2}

derivative of ln^2(1-2x)

\frac{d}{d x} (ln^{2} (1 - 2 x))

derivative f(x)= x/(ln(x))

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

y^{''}+6y^'+19y=0

y^{^{''}} + 6 y^{^{'}} + 19 y = 0