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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

\frac{9 \cdot 2}{n} - (\frac{n ( n + 1 ) ( 2 n + 1 )}{6}) (\frac{2}{n})^{3}

lo g_{10} (10) (x) - lo g_{10} (10) (x)

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

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

\frac{d}{d x} (- a (x) e^{b (x - 190)}) - 15

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