What is (\partial)/(\partial x)(xe^{-t}sin(θ)) ?

The answer to (\partial)/(\partial x)(xe^{-t}sin(θ)) is e^{-t}sin(θ)

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(\partial)/(\partial x)(xe^{-t}sin(θ))

\frac{\partial}{\partial x} (x e^{- t} sin (θ))

e^{- t} sin (θ)

Solution steps

\frac{\partial}{\partial x} (x e^{- t} sin (θ))

Treat

t, θ

as constants

Take the constant out:

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

= e^{- t} sin (θ) \frac{\partial}{\partial x} (x)

Apply the common derivative:

\frac{\partial}{\partial x} (x) = 1

= e^{- t} sin (θ) \cdot 1

Simplify

= e^{- t} sin (θ)

What is (\partial)/(\partial x)(xe^{-t}sin(θ)) ?
The answer to (\partial)/(\partial x)(xe^{-t}sin(θ)) is e^{-t}sin(θ)