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

The solution to expand (x+1)(dy)/(dx) is x(dy)/(dx)+(dy)/(dx)

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Multiply:

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

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

\frac{( 8 x - 3 ) ( x + 2 )}{( x + 3 ) ( 2 x - 3 )}

(e^{c} - y - 2 x)^{2}

- \frac{40}{( 4 t + 1 ) ^{2}}

\frac{1}{x + 1} - \frac{1}{x + 2}

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

What is expand (x+1)(dy)/(dx) ?
The solution to expand (x+1)(dy)/(dx) is x(dy)/(dx)+(dy)/(dx)