What is (\partial)/(\partial x)(e^{8x}cos(-9y)) ?

The answer to (\partial)/(\partial x)(e^{8x}cos(-9y)) is cos(9y)e^{8x}*8

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(\partial)/(\partial x)(e^{8x}cos(-9y))

\frac{\partial}{\partial x} (e^{8 x} cos (- 9 y))

cos (9 y) e^{8 x} \cdot 8

Solution steps

\frac{\partial}{\partial x} (e^{8 x} cos (- 9 y))

Simplify

e^{8 x} cos (- 9 y) : e^{8 x} cos (9 y)

= \frac{\partial}{\partial x} (e^{8 x} cos (9 y))

Treat

y

as a constant

Take the constant out:

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

= cos (9 y) \frac{\partial}{\partial x} (e^{8 x})

Apply the chain rule:

e^{8 x} \frac{\partial}{\partial x} (8 x)

= e^{8 x} \frac{\partial}{\partial x} (8 x)

\frac{\partial}{\partial x} (8 x) = 8

= cos (9 y) e^{8 x} \cdot 8

e^{- 6 x}

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\frac{1}{x + 1}

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What is (\partial)/(\partial x)(e^{8x}cos(-9y)) ?
The answer to (\partial)/(\partial x)(e^{8x}cos(-9y)) is cos(9y)e^{8x}*8