What is (\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y)) ?

The answer to (\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y)) is -4e^{-3pit}sin(4x)sin(6y)

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(\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y))

\frac{\partial}{\partial x} (e^{- 3 π t} cos (4 x) sin (6 y))

- 4 e^{- 3 π t} sin (4 x) sin (6 y)

Solution steps

\frac{\partial}{\partial x} (e^{- 3 π t} cos (4 x) sin (6 y))

Treat

t, y

as constants

Take the constant out:

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

= e^{- 3 π t} sin (6 y) \frac{\partial}{\partial x} (cos (4 x))

Apply the chain rule:

- sin (4 x) \frac{\partial}{\partial x} (4 x)

= - sin (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= e^{- 3 π t} sin (6 y) (- sin (4 x) \cdot 4)

Simplify

= - 4 e^{- 3 π t} sin (4 x) sin (6 y)

What is (\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y)) ?
The answer to (\partial)/(\partial x)(e^{-3pit}cos(4x)sin(6y)) is -4e^{-3pit}sin(4x)sin(6y)