What is expand e^y(1+x^2)y'(x)-x(1+e^y) ?

The solution to expand e^y(1+x^2)y'(x)-x(1+e^y) is e^yy'(x)+e^yx^2y'(x)-x-e^yx

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expand e^y(1+x^2)y'(x)-x(1+e^y)

expand

e^{y} (1 + x^{2}) y^{'} (x) - x (1 + e^{y})

e^{y} y' (x) + e^{y} x^{2} y' (x) - x - e^{y} x

Solution steps

e^{y} (1 + x^{2}) y^{'} (x) - x (1 + e^{y})

Expand

e^{y} y^{'} (x) (1 + x^{2}) : e^{y} y^{'} (x) + e^{y} x^{2} y^{'} (x)

= e^{y} y^{'} (x) + e^{y} x^{2} y^{'} (x) - x (1 + e^{y})

Expand

- x (1 + e^{y}) : - x - e^{y} x

= e^{y} y^{'} (x) + e^{y} x^{2} y^{'} (x) - x - e^{y} x

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

\frac{d}{d x} ((5) (x^{4} - \frac{10}{x}))

- \frac{t ( 1 + in )}{d t}

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

\frac{a ^{2} - 1}{a} - \frac{1}{a - 1}

What is expand e^y(1+x^2)y'(x)-x(1+e^y) ?
The solution to expand e^y(1+x^2)y'(x)-x(1+e^y) is e^yy'(x)+e^yx^2y'(x)-x-e^yx