What is (\partial)/(\partial t)(e^{-9t}cos(pix)) ?

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

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(\partial)/(\partial t)(e^{-9t}cos(pix))

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

- 9 e^{- 9 t} cos (π x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= cos (π x) e^{- 9 t} (- 9)

Simplify

= - 9 e^{- 9 t} cos (π x)

6 x (x + 3 y) y^{^{'}} = 6 y (x - 3 y)

\frac{d y}{d x} = x^{2} e^{- 4 x} - 4 y

x \to - 1 lim (2 x^{3} - 5 x + 6 x - 1)

\int (sec^{2} (x) + 9) d x

\int e^{x + 7} d x

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