What is (\partial)/(\partial x)(e^{-7x}cos(3pit)) ?

The answer to (\partial)/(\partial x)(e^{-7x}cos(3pit)) is -7e^{-7x}cos(3pit)

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(\partial)/(\partial x)(e^{-7x}cos(3pit))

\frac{\partial}{\partial x} (e^{- 7 x} cos (3 π t))

- 7 e^{- 7 x} cos (3 π t)

Solution steps

\frac{\partial}{\partial x} (e^{- 7 x} cos (3 π t))

Treat

t

as a constant

Take the constant out:

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

= cos (3 π t) \frac{\partial}{\partial x} (e^{- 7 x})

Apply the chain rule:

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

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

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

= cos (3 π t) e^{- 7 x} (- 7)

Simplify

= - 7 e^{- 7 x} cos (3 π t)

10 - 2 e^{x}

\frac{d}{d x} (sin (4 x - 5))

(\frac{x}{sin ( y )} + 2) d x + \frac{( x ^{2} + 1 ) cos ( y )}{cos ( 2 y ) - 1} d y = 0

\int e^{6 x + e^{6 x}} d x

(- 4.4) (- 6.6)

What is (\partial)/(\partial x)(e^{-7x}cos(3pit)) ?
The answer to (\partial)/(\partial x)(e^{-7x}cos(3pit)) is -7e^{-7x}cos(3pit)