What is (dx+e^{3x}dy)(e^{-3x}) ?

The solution to (dx+e^{3x}dy)(e^{-3x}) is (e^{3x}dy+dx)/(e^{3x)}

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simplify (dx+e^{3x}dy)(e^{-3x})

simplify

(d x + e^{3 x} d y) (e^{- 3 x})

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

Solution steps

(d x + e^{3 x} d y) (e^{- 3 x})

Apply exponent rule:

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

= \frac{1}{e ^{3 x}} (e^{3 x} d y + d x)

Multiply fractions:

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

= \frac{1 \cdot ( d x + e ^{3 x} d y )}{e ^{3 x}}

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

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

a + 1 a^{2} - 1

π

2 e^{- 1.25 π}

1.256 \cdot 1 0^{- 1}

(1 + e^{- 1.14})^{- 1}

What is (dx+e^{3x}dy)(e^{-3x}) ?
The solution to (dx+e^{3x}dy)(e^{-3x}) is (e^{3x}dy+dx)/(e^{3x)}