erweitern y'(x)(x^3-cos(x))^5

Lösung

erweitern

y^{'} (x) (x^{3} - cos (x))^{5}

x^{15} y' (x) - 5 x^{12} cos (x) y' (x) + 10 x^{9} cos^{2} (x) y' (x) - 10 x^{6} cos^{3} (x) y' (x) + 5 x^{3} cos^{4} (x) y' (x) - cos^{5} (x) y' (x)

Schritte zur Lösung

y^{'} (x) (x^{3} - cos (x))^{5}

(x^{3} - cos (x))^{5} = x^{15} - 5 x^{12} cos (x) + 10 x^{9} cos^{2} (x) - 10 x^{6} cos^{3} (x) + 5 x^{3} cos^{4} (x) - cos^{5} (x)

= y^{^{'}} (x) (x^{15} - 5 x^{12} cos (x) + 10 x^{9} cos^{2} (x) - 10 x^{6} cos^{3} (x) + 5 x^{3} cos^{4} (x) - cos^{5} (x))

Setze Klammern

= y^{^{'}} (x) x^{15} + y^{^{'}} (x) (- 5 x^{12} cos (x)) + y^{^{'}} (x) 10 x^{9} cos^{2} (x) + y^{^{'}} (x) (- 10 x^{6} cos^{3} (x)) + y^{^{'}} (x) 5 x^{3} cos^{4} (x) + y^{^{'}} (x) (- cos^{5} (x))

Wende Minus-Plus Regeln an

+ (- a) = - a

= x^{15} y^{^{'}} (x) - 5 x^{12} cos (x) y^{^{'}} (x) + 10 x^{9} cos^{2} (x) y^{^{'}} (x) - 10 x^{6} cos^{3} (x) y^{^{'}} (x) + 5 x^{3} cos^{4} (x) y^{^{'}} (x) - cos^{5} (x) y^{^{'}} (x)

e x p an d ln (3 z + 1)

e x p an d ((x + Δ x) - 1) (x - 1)

e x p an d a ((a - b) \cdot (a + 2 b))

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

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