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

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

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

\frac{\partial}{\partial x} (e^{- 9 x} cos (θ))

- 9 e^{- 9 x} cos (θ)

Solution steps

\frac{\partial}{\partial x} (e^{- 9 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^{- 9 x})

Apply the chain rule:

e^{- 9 x} \frac{\partial}{\partial x} (- 9 x)

= e^{- 9 x} \frac{\partial}{\partial x} (- 9 x)

\frac{\partial}{\partial x} (- 9 x) = - 9

= cos (θ) e^{- 9 x} (- 9)

Simplify

= - 9 e^{- 9 x} cos (θ)

\frac{s}{s ^{2} + 4 ^{2}}

\int \frac{e ^{x} + 9}{e ^{2 x} - 6 e ^{x} + 9} d x

f (x) = e^{7 x}

\frac{d}{d θ} (l^{2} - (l sin (θ) - x (θ))^{2} - l cos (θ))

\frac{d y}{d x} = \frac{4 x}{3 y}

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