What is the d/(dt)((x)(e^t+e^{-t})) ?

The d/(dt)((x)(e^t+e^{-t})) is x(e^t-e^{-t})

What is the first d/(dt)((x)(e^t+e^{-t})) ?

The first d/(dt)((x)(e^t+e^{-t})) is x(e^t-e^{-t})

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

x (e^{t} - e^{- t})

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{d}{d t} (e^{t} + e^{- t})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{d}{d t} (e^{t}) + \frac{d}{d t} (e^{- t}))

\frac{d}{d t} (e^{t}) = e^{t}

\frac{d}{d t} (e^{- t}) = - e^{- t}

= x (e^{t} - e^{- t})

4 x (2 x^{2} - 1 + C e^{- 2 x^{2}})

\frac{x ^{6}}{( x + 2 ) ( x - 2 )}

\frac{y - 3 x}{x ( x + 3 y + 2 )}

2 (y - 4 x^{2}) d x + x d y

\frac{d}{d t} ((x) (y + t))

What is the d/(dt)((x)(e^t+e^{-t})) ?
The d/(dt)((x)(e^t+e^{-t})) is x(e^t-e^{-t})
What is the first d/(dt)((x)(e^t+e^{-t})) ?
The first d/(dt)((x)(e^t+e^{-t})) is x(e^t-e^{-t})