What is (\partial)/(\partial t)(ae^{kx+wt}) ?

The answer to (\partial)/(\partial t)(ae^{kx+wt}) is ae^{kx+wt}w

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(\partial)/(\partial t)(ae^{kx+wt})

\frac{\partial}{\partial t} (a e^{k x + wt})

a e^{k x + wt} w

Solution steps

\frac{\partial}{\partial t} (a e^{k x + wt})

Treat

a, k, x, w

as constants

Take the constant out:

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

= a \frac{\partial}{\partial t} (e^{k x + wt})

Apply the chain rule:

e^{k x + wt} \frac{\partial}{\partial t} (k x + wt)

= e^{k x + wt} \frac{\partial}{\partial t} (k x + wt)

\frac{\partial}{\partial t} (k x + wt) = w

= a e^{k x + wt} w

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What is (\partial)/(\partial t)(ae^{kx+wt}) ?
The answer to (\partial)/(\partial t)(ae^{kx+wt}) is ae^{kx+wt}w