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Beliebt Rechnen >

derivative of (3x^5+8/(x^3))

Lösung

\frac{d}{d x} (\frac{3 x ^{5} + 8}{x ^{3}})

Lösung

\frac{6 ( x ^{5} - 4 )}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{5} + 8}{x ^{3}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x ^{5} + 8 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3 x ^{5} + 8 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3 x^{5} + 8) = 15 x^{4}

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

= \frac{15 x ^{4} x ^{3} - 3 x ^{2} ( 3 x ^{5} + 8 )}{( x ^{3} ) ^{2}}

Vereinfache

\frac{15 x ^{4} x ^{3} - 3 x ^{2} ( 3 x ^{5} + 8 )}{( x ^{3} ) ^{2}} : \frac{6 ( x ^{5} - 4 )}{x ^{4}}

= \frac{6 ( x ^{5} - 4 )}{x ^{4}}

Graph

Beliebte Beispiele

integral of 2xln(2x)

\int 2 x ln (2 x) d x

y^{''}-6y^'+10y=0

y^{^{''}} - 6 y^{^{'}} + 10 y = 0

derivative C(x)=(4x+50)/(x+2)

d er i v a t i v e C (x) = \frac{4 x + 50}{x + 2}

integral of (x+3)(x^2+1)

\int (x + 3) (x^{2} + 1) d x

integral of 4arcsin(x)

\int 4 arcsin (x) d x