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

The solution to expand-2(2xy+derivative of (yx^2)) is -4xy-2 derivative of x^2y

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expand-2(2xy+derivative of (yx^2))

expand

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

- 4 x y - 2 \frac{d}{d x} (x^{2} y)

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

- 2 \cdot 2 x y - 2 \frac{d}{d x} (x^{2} (y)) : - 4 x y - 2 \frac{d}{d x} (x^{2} y)

= - 4 x y - 2 \frac{d}{d x} (x^{2} y)

(2 x + 3) \circ (x^{2} - 2 x + 4)

\frac{( - x + 20 ) ( x - 10 )}{2}

\frac{3 t + 2}{t ( 1 + t ^{2} )}

\frac{10 ( 10 + 129 )}{29}

(4 - 5 x + 2 x^{2}) (1 + x, 1 - x, x^{2})

What is expand-2(2xy+derivative of (yx^2)) ?
The solution to expand-2(2xy+derivative of (yx^2)) is -4xy-2 derivative of x^2y