derivative of (2x^3-6pi^2/(x^5))

Lösung

\frac{d}{d x} (\frac{2 x ^{3} - 6 π ^{2}}{x ^{5}})

\frac{2 ( - 2 x ^{3} + 15 π ^{2} )}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{3} - 6 π ^{2}}{x ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{3} - 6 π ^{2} ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( 2 x ^{3} - 6 π ^{2} )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (2 x^{3} - 6 π^{2}) = 6 x^{2}

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

= \frac{6 x ^{2} x ^{5} - 5 x ^{4} ( 2 x ^{3} - 6 π ^{2} )}{( x ^{5} ) ^{2}}

Vereinfache

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

= \frac{2 ( - 2 x ^{3} + 15 π ^{2} )}{x ^{6}}

\int π cos (\frac{n x}{2}) d x

x \to 0 lim (- 7)

\frac{\partial}{\partial x} (e^{- x} cos (π t))

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

\frac{1}{2} x^{3} + 2, x + 1, x = 0, x = 2