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

The answer to (\partial)/(\partial x)(-5e^{-5y}sin(5x)) is -25e^{-5y}cos(5x)

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

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

- 25 e^{- 5 y} cos (5 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= - 5 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

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

Simplify

= - 25 e^{- 5 y} cos (5 x)

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\frac{d}{d x} (2 e^{c o s (\frac{x}{2})})

\frac{( x ^{2} - 3 x )}{x + 1}

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What is (\partial)/(\partial x)(-5e^{-5y}sin(5x)) ?
The answer to (\partial)/(\partial x)(-5e^{-5y}sin(5x)) is -25e^{-5y}cos(5x)