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

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

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

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

- 5 e^{- 5 y} sin (5 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (5 x) \frac{\partial}{\partial x} (5 x)

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

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

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

Simplify

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

y = \frac{24}{x ^{4}}

\frac{d}{d x} (3 sin^{4} (x))

\frac{d ^{2} x}{d t ^{2}} + a x = 0

\frac{d}{d x} (1 - 2 x + 3 x^{2} - 4 x^{3})

\int e^{0.2 x} d x

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