What is (\partial)/(\partial t)((y)(2y+e^{2t})) ?

The answer to (\partial)/(\partial t)((y)(2y+e^{2t})) is 2e^{2t}y

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(\partial)/(\partial t)((y)(2y+e^{2t}))

\frac{\partial}{\partial t} ((y) (2 y + e^{2 t}))

2 e^{2 t} y

Solution steps

\frac{\partial}{\partial t} ((y) (2 y + e^{2 t}))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial t} (2 y + e^{2 t})

Apply the Sum/Difference Rule:

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

= y (\frac{\partial}{\partial t} (2 y) + \frac{\partial}{\partial t} (e^{2 t}))

\frac{\partial}{\partial t} (2 y) = 0

\frac{\partial}{\partial t} (e^{2 t}) = e^{2 t} \cdot 2

= y (0 + e^{2 t} \cdot 2)

Simplify

= 2 e^{2 t} y

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What is (\partial)/(\partial t)((y)(2y+e^{2t})) ?
The answer to (\partial)/(\partial t)((y)(2y+e^{2t})) is 2e^{2t}y