erweitern (x-y/(y'(x)))^2+(y-xy'(x))^2

Lösung

erweitern

(x - \frac{y}{y ^{'} ( x )})^{2} + (y - x y^{'} (x))^{2}

x^{2} - \frac{2 x y}{y ' ( x )} + \frac{y ^{2}}{( y ' ( x ) ) ^{2}} + y^{2} - 2 x yy' (x) + x^{2} (y' (x))^{2}

Schritte zur Lösung

(x - \frac{y}{y ^{'} ( x )})^{2} + (y - x y^{'} (x))^{2}

(x - \frac{y}{y ^{'} ( x )})^{2} : x^{2} - \frac{2 x y}{y ^{'} ( x )} + \frac{y ^{2}}{( y ^{'} ( x ) ) ^{2}}

= x^{2} - \frac{2 x y}{y ^{'} ( x )} + \frac{y ^{2}}{( y ^{'} ( x ) ) ^{2}} + (y - x y^{'} (x))^{2}

(y - x y^{'} (x))^{2} : y^{2} - 2 x y y^{'} (x) + x^{2} (y^{'} (x))^{2}

= x^{2} - \frac{2 x y}{y ^{'} ( x )} + \frac{y ^{2}}{( y ^{'} ( x ) ) ^{2}} + y^{2} - 2 x y y^{'} (x) + x^{2} (y^{'} (x))^{2}

e x p an d \frac{1}{s ( t s + 1 )}

s im pl i f y (x - 3) (x - \frac{5}{2})

e x p an d (5 + cos (x)) cos (y) cos (x)

e x p an d (x + y)^{2} (x \frac{d y}{d x} + y)

s im pl i f y (x^{2} + y^{2}) (x^{2} + y^{2})