What is (\partial)/(\partial x)(sin(4y)e^{-5x}) ?

The answer to (\partial)/(\partial x)(sin(4y)e^{-5x}) is -5e^{-5x}sin(4y)

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(\partial)/(\partial x)(sin(4y)e^{-5x})

\frac{\partial}{\partial x} (sin (4 y) e^{- 5 x})

- 5 e^{- 5 x} sin (4 y)

Solution steps

\frac{\partial}{\partial x} (sin (4 y) e^{- 5 x})

Treat

y

as a constant

Take the constant out:

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

= sin (4 y) \frac{\partial}{\partial x} (e^{- 5 x})

Apply the chain rule:

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

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

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

= sin (4 y) e^{- 5 x} (- 5)

Simplify

= - 5 e^{- 5 x} sin (4 y)

f (x) = - x^{3} - 150 x^{2} + 60000 x - 800

\int e^{x} (sin (x) + cos (x)) d x

\frac{\partial}{\partial y} (x - 4 y - 9)

\int (4 + 3 x)^{4} d x

n = 1 \sum \infty \frac{n - 1}{2 n + 1}

What is (\partial)/(\partial x)(sin(4y)e^{-5x}) ?
The answer to (\partial)/(\partial x)(sin(4y)e^{-5x}) is -5e^{-5x}sin(4y)