What is (\partial)/(\partial x)(e^{-5y}sin(5x)) ?

The answer to (\partial)/(\partial x)(e^{-5y}sin(5x)) is e^{-5y}cos(5x)*5

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(\partial)/(\partial x)(e^{-5y}sin(5x))

\frac{\partial}{\partial x} (e^{- 5 y} sin (5 x))

e^{- 5 y} cos (5 x) \cdot 5

Solution steps

\frac{\partial}{\partial x} (e^{- 5 y} sin (5 x))

Treat

y

as a constant

Take the constant out:

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

= e^{- 5 y} \frac{\partial}{\partial x} (sin (5 x))

Apply the chain rule:

cos (5 x) \frac{\partial}{\partial x} (5 x)

= cos (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= e^{- 5 y} cos (5 x) \cdot 5

What is (\partial)/(\partial x)(e^{-5y}sin(5x)) ?
The answer to (\partial)/(\partial x)(e^{-5y}sin(5x)) is e^{-5y}cos(5x)*5