What is expand (y^2+1)(dy)/(dx) ?

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

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expand (y^2+1)(dy)/(dx)

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{d y}{d x}, b = y^{2}, c = 1

= \frac{d y}{d x} y^{2} + \frac{d y}{d x} 1

= \frac{d y}{d x} y^{2} + 1 \frac{d y}{d x}

Multiply:

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

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

\frac{( x + h ) ^{2}}{h}

\frac{8 x + 4 + x ^{2}}{3 x ^{3} ( 2 x + 1 )}

\frac{4 x ^{2} + 20 x + 11}{( x - 3 ) ( x + 4 ) ( x + 5 )}

\frac{1}{x ( x ^{2} + 2 x - 1 )}

40 (\frac{3 x - 15}{1})

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