What is e^{-y}(1+(dy)/(dx)) ?

The solution to e^{-y}(1+(dy)/(dx)) is (\frac{dy)/(dx)+1}{e^y}

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simplify e^{-y}(1+(dy)/(dx))

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

(1.7) (1 0^{- 5}) (0.01)

0.6 e^{- 2 t}

8.85 x 1 0^{12} (100 m m^{2})

15 + h \cdot 15

(e^{x} - 1)^{4}

What is e^{-y}(1+(dy)/(dx)) ?
The solution to e^{-y}(1+(dy)/(dx)) is (\frac{dy)/(dx)+1}{e^y}