What is the (e^t(5-3e^{-2t}))^' ?

The (e^t(5-3e^{-2t}))^' is 5e^t+3e^{-t}

What is the first (e^t(5-3e^{-2t}))^' ?

The first (e^t(5-3e^{-2t}))^' is 5e^t+3e^{-t}

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(e^{t} (5 - 3 e^{- 2 t}))^{^{'}}

5 e^{t} + 3 e^{- t}

Solution steps

(e^{t} (5 - 3 e^{- 2 t}))^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{t}, g = 5 - 3 e^{- 2 t}

= (e^{t})^{^{'}} (5 - 3 e^{- 2 t}) + (5 - 3 e^{- 2 t})^{^{'}} e^{t}

(e^{t})^{'} = e^{t}

(5 - 3 e^{- 2 t})^{'} = 6 e^{- 2 t}

= e^{t} (5 - 3 e^{- 2 t}) + 6 e^{- 2 t} e^{t}

Simplify

e^{t} (5 - 3 e^{- 2 t}) + 6 e^{- 2 t} e^{t} : 5 e^{t} + 3 e^{- t}

= 5 e^{t} + 3 e^{- t}

\int 12 x^{3} d x

250

x \to 0 lim (x + 1)

x \to 0 lim (\frac{( e ^{x} - 1 )}{x})

\int (4 x^{3} - 3 x^{2} + 6 x - 1) d x

What is the (e^t(5-3e^{-2t}))^' ?
The (e^t(5-3e^{-2t}))^' is 5e^t+3e^{-t}
What is the first (e^t(5-3e^{-2t}))^' ?
The first (e^t(5-3e^{-2t}))^' is 5e^t+3e^{-t}