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

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

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

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

- 2 e^{- 2 x} cos (θ)

Solution steps

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

Treat

θ

as a constant

Take the constant out:

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

= cos (θ) \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 (θ) e^{- 2 x} (- 2)

Simplify

= - 2 e^{- 2 x} cos (θ)

x \to 0 lim (1 - \frac{sin ( x )}{x})

\frac{d}{d x} (\frac{2 x ^{2}}{∣ x ∣})

\frac{d}{d x} (1 - e^{x})

y = x^{3} - 2 x + 2 (4.58)

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