What is expand 5(2xy^2+2y derivative of (yx^2)) ?

The solution to expand 5(2xy^2+2y derivative of (yx^2)) is 10xy^2+10y derivative of x^2y

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

expand

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)

Solution steps

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)))

Apply the distributive law:

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))

Simplify

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)

r (2, 2, - 1) \cdot s (1, - 2, 3)

ln (7 x^{2})

\frac{( ( λ - 1 ) ( 4 λ - 3 ) )}{4}

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

\frac{s + a + 1}{( s + a ) ( s + 2 ) ^{2}}

What is expand 5(2xy^2+2y derivative of (yx^2)) ?
The solution to expand 5(2xy^2+2y derivative of (yx^2)) is 10xy^2+10y derivative of x^2y