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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot y^{3} = y^{3}

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

2 (π 2^{2})

\frac{d}{d x} ((d) 60 d (4 + x)^{- 1})

e^{- 2} 2^{0} (\frac{1}{0 !})

(4.9 x 1 0^{- 2}) (4 x 1 0^{- 1})

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

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