What is expand e^{x^2}((dy)/(dx)+2xy) ?

The solution to expand e^{x^2}((dy)/(dx)+2xy) is e^{x^2}(dy)/(dx)+2e^{x^2}xy

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expand e^{x^2}((dy)/(dx)+2xy)

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

1 6^{(\frac{1}{2})}

\frac{a}{( s + b ) ( s + a )}

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

\frac{2 ( 4 x - 14 ) ^{2}}{9}

8 (x + Δ x)^{2}

What is expand e^{x^2}((dy)/(dx)+2xy) ?
The solution to expand e^{x^2}((dy)/(dx)+2xy) is e^{x^2}(dy)/(dx)+2e^{x^2}xy