derivative y=((x+b)(x-a))/((x-b))

Lösung

ableitung von

y = \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 t \cdot sec^{2} (2 t) d t

\int \frac{cos ^{3} ( 4 x )}{sin ( 4 x )} d x

3 x^{2} y^{2} d x + (2 y^{3} + 4 y^{3}) d y = 0

\frac{\partial}{\partial x} (x^{7} y^{5} - x^{6} y^{4})

in v erse l a pl a ce \frac{3}{5 s - 2}