derivative of (pisqrt(8100+x^2)/x)

Lösung

\frac{d}{d x} (\frac{π 8100 + x ^{2}}{x})

- \frac{8100 π}{x ^{2} 8100 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{π 8100 + x ^{2}}{x})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= π \frac{d}{d x} (\frac{8100 + x ^{2}}{x})

Wende die Quotientenregel an:

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

= π \frac{\frac{d}{d x} ( 8100 + x ^{2} ) x - \frac{d x}{d x} 8100 + x ^{2}}{x ^{2}}

\frac{d}{d x} (8100 + x^{2}) = \frac{x}{8100 + x ^{2}}

\frac{d x}{d x} = 1

= π \frac{\frac{x}{8100 + x ^{2}} x - 1 \cdot 8100 + x ^{2}}{x ^{2}}

Vereinfache

π \frac{\frac{x}{8100 + x ^{2}} x - 1 \cdot 8100 + x ^{2}}{x ^{2}} : - \frac{8100 π}{x ^{2} 8100 + x ^{2}}

= - \frac{8100 π}{x ^{2} 8100 + x ^{2}}

d er i v a t i v e \frac{4}{x + 10}

x \to + 1 + lim (\frac{5}{x ^{3} - 1})

a re a f (x) = 8 x + 2 x^{2} - x^{3}, g (x) = 0

\int \frac{sec ( y )}{co tan ( y )} d y

2 x y y^{^{'}} = y^{2} - x^{2}