derivative of (2x^5-15/(x^4))

Lösung

\frac{d}{d x} (\frac{2 x ^{5} - 15}{x ^{4}})

\frac{2 ( x ^{5} + 30 )}{x ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{5} - 15}{x ^{4}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{5} - 15 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 2 x ^{5} - 15 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (2 x^{5} - 15) = 10 x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{10 x ^{4} x ^{4} - 4 x ^{3} ( 2 x ^{5} - 15 )}{( x ^{4} ) ^{2}}

Vereinfache

\frac{10 x ^{4} x ^{4} - 4 x ^{3} ( 2 x ^{5} - 15 )}{( x ^{4} ) ^{2}} : \frac{2 ( x ^{5} + 30 )}{x ^{5}}

= \frac{2 ( x ^{5} + 30 )}{x ^{5}}

x \to - 1 lim (3 x)

d er i v a t i v e e^{6 y}

\frac{d}{d x} (sin (3 x) + cos (2 x))

\int_{0}^{1} \frac{2 x ^{2}}{1 + x ^{2}} d x

d er i v a t i v e 1 - x^{2}