derivative of (2x^5+3x^4-x^3+2/(x^2))

Lösung

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - x ^{3} + 2}{x ^{2}})

\frac{6 x ^{5} + 6 x ^{4} - x ^{3} - 4}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - x ^{3} + 2}{x ^{2}})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (2 x^{5} + 3 x^{4} - x^{3} + 2) = 10 x^{4} + 12 x^{3} - 3 x^{2}

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

= \frac{( 10 x ^{4} + 12 x ^{3} - 3 x ^{2} ) x ^{2} - 2 x ( 2 x ^{5} + 3 x ^{4} - x ^{3} + 2 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{( 10 x ^{4} + 12 x ^{3} - 3 x ^{2} ) x ^{2} - 2 x ( 2 x ^{5} + 3 x ^{4} - x ^{3} + 2 )}{( x ^{2} ) ^{2}} : \frac{6 x ^{5} + 6 x ^{4} - x ^{3} - 4}{x ^{3}}

= \frac{6 x ^{5} + 6 x ^{4} - x ^{3} - 4}{x ^{3}}

\int_{0}^{3} 2 x - 1 d x

\int \frac{3}{2} x^{\frac{1}{2}} d x

x \to 1 lim (- 2 1 - x + 2)

\frac{d}{d x} (sin (x^{2} + 2 x))

x \to 0 lim (cos (x) ln (x))