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

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

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

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

- e^{- t} x sin (θ)

Solution steps

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

Treat

x, θ

as constants

Take the constant out:

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

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

Apply the chain rule:

e^{- t} \frac{\partial}{\partial t} (- t)

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

\frac{\partial}{\partial t} (- t) = - 1

= x sin (θ) e^{- t} (- 1)

Simplify

= - e^{- t} x sin (θ)

x \to 0 + lim (\frac{1}{x ^{2}} + ln (x))

\int \frac{- 10}{x ^{2} ( 25 - x ^{2} ) ^{\frac{1}{2}}} d x

x (x - 8)

\int x^{2} e^{18 x} d x

\int 4 x d x

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