What is (dx)/x x/(1+y^2)e^{-xy} ?

The solution to (dx)/x x/(1+y^2)e^{-xy} is (dx)/(e^{xy)(y^2+1)}

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simplify (dx)/x x/(1+y^2)e^{-xy}

simplify

\frac{d x}{x} \frac{x}{1 + y ^{2}} e^{- x y}

\frac{d x}{e ^{x y} ( y ^{2} + 1 )}

Solution steps

\frac{d x}{x} \cdot \frac{x}{1 + y ^{2}} e^{- x y}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{x y}} \cdot \frac{x}{y ^{2} + 1} \cdot \frac{d x}{x}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{d xx \cdot 1}{x ( 1 + y ^{2} ) e ^{x y}}

Cancel the common factor:

x

= \frac{d x \cdot 1}{( 1 + y ^{2} ) e ^{x y}}

Multiply:

d x \cdot 1 = d x

= \frac{d x}{e ^{x y} ( y ^{2} + 1 )}

e^{- 4 x} \cdot e^{4 x}

42 x

(4.2 \cdot 1 0^{- 6}) (6 \cdot 1 0^{- 4})

(3 \cdot 1 0^{9}) (4.7 \cdot 1 0^{- 4})

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

What is (dx)/x x/(1+y^2)e^{-xy} ?
The solution to (dx)/x x/(1+y^2)e^{-xy} is (dx)/(e^{xy)(y^2+1)}