derivative of (2x^5+8/(x^3))

Lösung

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

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

Schritte zur Lösung

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

\frac{d}{d x} (2 x^{5} + 8) = 10 x^{4}

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

= \frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}}

Vereinfache

\frac{10 x ^{4} x ^{3} - 3 x ^{2} ( 2 x ^{5} + 8 )}{( x ^{3} ) ^{2}} : \frac{4 ( x ^{5} - 6 )}{x ^{4}}

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

d er i v a t i v e 15 x ln (14 x)

n = 2 \sum \infty \frac{3 n}{n ^{2} - 2}

x \to 5 + lim (\frac{6 x}{x - 5})

\int 3 x 5 x^{2} + 1 d x

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