erweitern (x^2+1)y'(x)

Lösung

erweitern

(x^{2} + 1) y^{'} (x)

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

Schritte zur Lösung

(x^{2} + 1) y^{'} (x)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = y^{'} (x), b = x^{2}, c = 1

= y^{^{'}} (x) x^{2} + y^{^{'}} (x) 1

= x^{2} y^{^{'}} (x) + 1 y^{^{'}} (x)

Multipliziere:

1 y^{'} (x) = y^{'} (x)

= x^{2} y^{^{'}} (x) + y^{^{'}} (x)

e x p an d \frac{2 ( 715 - p ) ^{2}}{5}

e x p an d \frac{a ^{2} + b ^{2} + c ^{2} + 3 ab c}{( a + b ) ( b + c ) ( c + a )}

e x p an d \frac{18}{s ( s ^{2} + 36 )}

e x p an d \frac{10}{( s + 10 ) ( s ^{2} + 2 s + 1 )}

e x p an d \frac{( x + 1 )}{( x - 1 )} - \frac{x}{( x + 2 )}