derivative of ((x+b(x-a))/((x-b)))

Lösung

\frac{d}{d x} (\frac{( x + b ) ( x - a )}{( x - b )})

\frac{x ^{2} - 2 b x - b ^{2} + 2 ba}{( x - b ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x + b ) ( x - a )}{( x - b )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x + b ) ( x - a ) ) ( x - b ) - \frac{d}{d x} ( x - b ) ( x + b ) ( x - a )}{( x - b ) ^{2}}

\frac{d}{d x} ((x + b) (x - a)) = 2 x + b - a

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

= \frac{( 2 x + b - a ) ( x - b ) - 1 \cdot ( x + b ) ( x - a )}{( x - b ) ^{2}}

Vereinfache

\frac{( 2 x + b - a ) ( x - b ) - 1 \cdot ( x + b ) ( x - a )}{( x - b ) ^{2}} : \frac{x ^{2} - 2 b x - b ^{2} + 2 ba}{( x - b ) ^{2}}

= \frac{x ^{2} - 2 b x - b ^{2} + 2 ba}{( x - b ) ^{2}}

\int_{0}^{x^{2}} sin (t^{3}) d t

\frac{d}{d x} (cos (a^{3} + x^{3}))

\int sec (3 t) d t

x \to - 1 lim (5)

\frac{d}{d x} (x^{\frac{1}{2}} + 4 x^{\frac{2}{3}} + 7 x + 3)