What is expand 1/25 (e^{5t}*5t-e^{-5t}) ?

The solution to expand 1/25 (e^{5t}*5t-e^{-5t}) is (e^{5t}t)/5-1/25 e^{-5t}

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expand 1/25 (e^{5t}*5t-e^{-5t})

expand

\frac{1}{25} (e^{5 t} \cdot 5 t - e^{- 5 t})

\frac{e ^{5 t} t}{5} - \frac{1}{25} e^{- 5 t}

Solution steps

\frac{1}{25} (e^{5 t} \cdot 5 t - e^{- 5 t})

= \frac{1}{25} (5 e^{5 t} t - e^{- 5 t})

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{25}, b = e^{5 t} \cdot 5 t, c = e^{- 5 t}

= \frac{1}{25} e^{5 t} \cdot 5 t - \frac{1}{25} e^{- 5 t}

= 5 \cdot \frac{1}{25} e^{5 t} t - \frac{1}{25} e^{- 5 t}

Simplify

5 \cdot \frac{1}{25} e^{5 t} t - \frac{1}{25} e^{- 5 t} : \frac{e ^{5 t} t}{5} - \frac{1}{25} e^{- 5 t}

= \frac{e ^{5 t} t}{5} - \frac{1}{25} e^{- 5 t}

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What is expand 1/25 (e^{5t}*5t-e^{-5t}) ?
The solution to expand 1/25 (e^{5t}*5t-e^{-5t}) is (e^{5t}t)/5-1/25 e^{-5t}