derivative of (x+4/(x-3))

Lösung

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

- \frac{7}{( x - 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x + 4) = 1

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

= \frac{1 \cdot ( x - 3 ) - 1 \cdot ( x + 4 )}{( x - 3 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 3 ) - 1 \cdot ( x + 4 )}{( x - 3 ) ^{2}} : - \frac{7}{( x - 3 ) ^{2}}

= - \frac{7}{( x - 3 ) ^{2}}

d er i v a t i v e cos^{9} (x)

x \to - 5 + lim (25 - x^{2})

y^{^{''}} + y = cos (3 t), y (0) = 1, y^{^{'}} (0) = 0

d er i v a t i v e f (x) = 8 x

s l o p e x^{4} - 13 x^{2} + 36