What is (\partial)/(\partial x)(e^{-7x}cos(10x)) ?

The answer to (\partial)/(\partial x)(e^{-7x}cos(10x)) is -7e^{-7x}cos(10x)-10e^{-7x}sin(10x)

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(\partial)/(\partial x)(e^{-7x}cos(10x))

\frac{\partial}{\partial x} (e^{- 7 x} cos (10 x))

- 7 e^{- 7 x} cos (10 x) - 10 e^{- 7 x} sin (10 x)

Solution steps

\frac{\partial}{\partial x} (e^{- 7 x} cos (10 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- 7 x}, g = cos (10 x)

= \frac{\partial}{\partial x} (e^{- 7 x}) cos (10 x) + \frac{\partial}{\partial x} (cos (10 x)) e^{- 7 x}

\frac{\partial}{\partial x} (e^{- 7 x}) = - 7 e^{- 7 x}

\frac{\partial}{\partial x} (cos (10 x)) = - sin (10 x) \cdot 10

= (- 7 e^{- 7 x}) cos (10 x) + (- sin (10 x) \cdot 10) e^{- 7 x}

Simplify

= - 7 e^{- 7 x} cos (10 x) - 10 e^{- 7 x} sin (10 x)

f (x) = 10 - 4 e^{x}, (0, 6)

\frac{d}{d x} (sin (4))

\frac{d}{d x} (ln (x - 1) + 1)

x \to 2 lim (x ln (\frac{x}{x - 2}))

f (x) = 4 x^{2} + 5 x + 17

What is (\partial)/(\partial x)(e^{-7x}cos(10x)) ?
The answer to (\partial)/(\partial x)(e^{-7x}cos(10x)) is -7e^{-7x}cos(10x)-10e^{-7x}sin(10x)