What is expand xy(1+xy)(dy)/(dx) ?

The solution to expand xy(1+xy)(dy)/(dx) is xy(dy)/(dx)+x^2y^2(dy)/(dx)

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expand xy(1+xy)(dy)/(dx)

expand

x y (1 + x y) \frac{d y}{d x}

x y \frac{d y}{d x} + x^{2} y^{2} \frac{d y}{d x}

Solution steps

x y (1 + x y) \frac{d y}{d x}

Apply the distributive law:

a (b + c) = ab + a c

a = x y \frac{d y}{d x}, b = 1, c = x y

= x y \frac{d y}{d x} 1 + x y \frac{d y}{d x} x y

= 1 \cdot x y \frac{d y}{d x} + xx yy \frac{d y}{d x}

Simplify

1 \cdot x y \frac{d y}{d x} + xx yy \frac{d y}{d x} : x y \frac{d y}{d x} + x^{2} y^{2} \frac{d y}{d x}

= x y \frac{d y}{d x} + x^{2} y^{2} \frac{d y}{d x}

d i s t r ib u t e - 4 x - 2 (x + h)

2 (a - 2 e)

e^{\frac{2 πi ( n - 1 )}{n}}

(\frac{( - 3 x - 2 ) ^{2} x}{6 x - 3}) - 1

(4 e^{6 t} - e^{8 t}) 6 e^{6 t}

What is expand xy(1+xy)(dy)/(dx) ?
The solution to expand xy(1+xy)(dy)/(dx) is xy(dy)/(dx)+x^2y^2(dy)/(dx)