What is (\partial)/(\partial x)(e^{-2x}cos(9pit)) ?

The answer to (\partial)/(\partial x)(e^{-2x}cos(9pit)) is -2e^{-2x}cos(9pit)

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(\partial)/(\partial x)(e^{-2x}cos(9pit))

\frac{\partial}{\partial x} (e^{- 2 x} cos (9 π t))

- 2 e^{- 2 x} cos (9 π t)

Solution steps

\frac{\partial}{\partial x} (e^{- 2 x} cos (9 π t))

Treat

t

as a constant

Take the constant out:

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

= cos (9 π t) \frac{\partial}{\partial x} (e^{- 2 x})

Apply the chain rule:

e^{- 2 x} \frac{\partial}{\partial x} (- 2 x)

= e^{- 2 x} \frac{\partial}{\partial x} (- 2 x)

\frac{\partial}{\partial x} (- 2 x) = - 2

= cos (9 π t) e^{- 2 x} (- 2)

Simplify

= - 2 e^{- 2 x} cos (9 π t)

\int_{0}^{π} 7 sin^{2} (4 x) d x

\frac{d}{d t} (2 cos (2 t))

\frac{d}{d x} (\frac{x}{5 x + 8})

x \to - 2 + lim (\frac{1 - x}{x + 2})

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

What is (\partial)/(\partial x)(e^{-2x}cos(9pit)) ?
The answer to (\partial)/(\partial x)(e^{-2x}cos(9pit)) is -2e^{-2x}cos(9pit)