What is expand e^{3xy}*3(y+x(dy)/(dx)) ?

The solution to expand e^{3xy}*3(y+x(dy)/(dx)) is 3e^{3xy}y+3e^{3xy}x(dy)/(dx)

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expand e^{3xy}*3(y+x(dy)/(dx))

expand

e^{3 x y} \cdot 3 (y + x \frac{d y}{d x})

3 e^{3 x y} y + 3 e^{3 x y} x \frac{d y}{d x}

Solution steps

e^{3 x y} \cdot 3 (y + x \frac{d y}{d x})

= 3 e^{3 x y} (y + x \frac{d y}{d x})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{3 x y} \cdot 3, b = y, c = x \frac{d y}{d x}

= e^{3 x y} \cdot 3 y + e^{3 x y} \cdot 3 x \frac{d y}{d x}

= 3 e^{3 x y} y + 3 e^{3 x y} x \frac{d y}{d x}

50 (24 - 23 e^{- \frac{t}{200}})

Z ((n + 1) (- 2)^{n})

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

\frac{1}{( y - m ) ( y - n )}

- \frac{2 x ^{2} + 5 x + 9}{( x ^{2} + 7 ) ( x - 1 )}

What is expand e^{3xy}*3(y+x(dy)/(dx)) ?
The solution to expand e^{3xy}*3(y+x(dy)/(dx)) is 3e^{3xy}y+3e^{3xy}x(dy)/(dx)