What is (-5e^{-sin(x)})e^{-sin(x)} ?

The solution to (-5e^{-sin(x)})e^{-sin(x)} is -5/(e^{2sin(x))}

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simplify (-5e^{-sin(x)})e^{-sin(x)}

simplify

(- 5 e^{- s i n (x)}) e^{- s i n (x)}

- \frac{5}{e ^{2 s i n (x)}}

Solution steps

(- 5 e^{- s i n (x)}) e^{- s i n (x)}

Apply exponent rule:

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

= \frac{1}{e ^{s i n (x)}} (- 5 e^{- s i n (x)})

Remove parentheses:

(- a) = - a

= - 5 e^{- s i n (x)} \frac{1}{e ^{s i n (x)}}

Multiply fractions:

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

= - \frac{1 \cdot 5 e ^{- s i n (x)}}{e ^{s i n (x)}}

Multiply the numbers:

1 \cdot 5 = 5

= - \frac{5 e ^{- s i n (x)}}{e ^{s i n (x)}}

Apply exponent rule:

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

\frac{e ^{- s i n (x)}}{e ^{s i n (x)}} = e^{- s i n (x) - s i n (x)} = e^{- 2 s i n (x)}

= - \frac{5}{e ^{2 s i n (x)}}

(e^{x} x - e^{x}) \cdot e^{- x}

(3 x^{2}) \cdot (2 x)

sin (2 t) e^{- s t}

What is (-5e^{-sin(x)})e^{-sin(x)} ?
The solution to (-5e^{-sin(x)})e^{-sin(x)} is -5/(e^{2sin(x))}