derivative of (25x^2-1/(x+3))

Lösung

\frac{d}{d x} (\frac{25 x ^{2} - 1}{x + 3})

\frac{25 x ^{2} + 150 x + 1}{( x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{25 x ^{2} - 1}{x + 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 25 x ^{2} - 1 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( 25 x ^{2} - 1 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (25 x^{2} - 1) = 50 x

\frac{d}{d x} (x + 3) = 1

= \frac{50 x ( x + 3 ) - 1 \cdot ( 25 x ^{2} - 1 )}{( x + 3 ) ^{2}}

Vereinfache

\frac{50 x ( x + 3 ) - 1 \cdot ( 25 x ^{2} - 1 )}{( x + 3 ) ^{2}} : \frac{25 x ^{2} + 150 x + 1}{( x + 3 ) ^{2}}

= \frac{25 x ^{2} + 150 x + 1}{( x + 3 ) ^{2}}

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

z \to 0 lim (z^{3} e^{\frac{1}{z}})

\int_{1}^{2} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x

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

t an g e n t f (x) = x^{3} + x, at x = 0