erweitern 5(2xy^2+2y derivative of (yx^2))

Lösung

erweitern

5 (2 x y^{2} + 2 y \frac{d}{d x} ((y) x^{2}))

10 x y^{2} + 10 y \frac{d}{d x} (x^{2} y)

Schritte zur Lösung

5 (2 x y^{2} + 2 y \frac{d}{d x} ((y) x^{2}))

= 5 (2 x y^{2} + 2 y \frac{d}{d x} (x^{2} (y)))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = 5, b = 2 x y^{2}, c = 2 y \frac{d}{d x} ((y) x^{2})

= 5 \cdot 2 x y^{2} + 5 \cdot 2 y \frac{d}{d x} ((y) x^{2})

= 5 \cdot 2 x y^{2} + 5 \cdot 2 y \frac{d}{d x} (x^{2} (y))

Vereinfache

5 \cdot 2 x y^{2} + 5 \cdot 2 y \frac{d}{d x} (x^{2} (y)) : 10 x y^{2} + 10 y \frac{d}{d x} (x^{2} y)

= 10 x y^{2} + 10 y \frac{d}{d x} (x^{2} y)

e x p an d r (2, 2, - 1) \cdot s (1, - 2, 3)

e x p an d ln (7 x^{2})

e x p an d \frac{( ( λ - 1 ) ( 4 λ - 3 ) )}{4}

e x p an d (x^{2} - y^{5}) d x + (x^{2} - 5 x y) d y

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