What is the d/(dt)((x)(7ce^{5t}+ce^{-3t})) ?

The d/(dt)((x)(7ce^{5t}+ce^{-3t})) is x(35ce^{5t}-3ce^{-3t})

What is the first d/(dt)((x)(7ce^{5t}+ce^{-3t})) ?

The first d/(dt)((x)(7ce^{5t}+ce^{-3t})) is x(35ce^{5t}-3ce^{-3t})

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\frac{d}{d t} ((x) (7 c e^{5 t} + c e^{- 3 t}))

x (35 c e^{5 t} - 3 c e^{- 3 t})

Solution steps

\frac{d}{d t} ((x) (7 c e^{5 t} + c e^{- 3 t}))

Treat

c, x

as a constant

Take the constant out:

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

= x \frac{d}{d t} (7 c e^{5 t} + c e^{- 3 t})

Apply the Sum/Difference Rule:

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

= x (\frac{d}{d t} (7 c e^{5 t}) + \frac{d}{d t} (c e^{- 3 t}))

\frac{d}{d t} (7 c e^{5 t}) = 35 c e^{5 t}

\frac{d}{d t} (c e^{- 3 t}) = - 3 c e^{- 3 t}

= x (35 c e^{5 t} - 3 c e^{- 3 t})

(3 u - \frac{3}{23} v)^{2}

\frac{2 ( q + h ) ^{4} ln ( q + h ) - 2 q ^{4} ln ( q )}{h}

- \frac{- 9 x + 1}{x ( - x + 1 )}

(2 x) l e f t (3 x + 2)

ρ (y_{t - 1} = β x_{t - 1} + u_{t - 1} (ρ, y, t, x))

What is the d/(dt)((x)(7ce^{5t}+ce^{-3t})) ?
The d/(dt)((x)(7ce^{5t}+ce^{-3t})) is x(35ce^{5t}-3ce^{-3t})
What is the first d/(dt)((x)(7ce^{5t}+ce^{-3t})) ?
The first d/(dt)((x)(7ce^{5t}+ce^{-3t})) is x(35ce^{5t}-3ce^{-3t})