What is (\partial)/(\partial x)(e^{2x}cos(3y)) ?

The answer to (\partial)/(\partial x)(e^{2x}cos(3y)) is cos(3y)e^{2x}*2

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(\partial)/(\partial x)(e^{2x}cos(3y))

\frac{\partial}{\partial x} (e^{2 x} cos (3 y))

cos (3 y) e^{2 x} \cdot 2

Solution steps

\frac{\partial}{\partial x} (e^{2 x} cos (3 y))

Treat

y

as a constant

Take the constant out:

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

= cos (3 y) \frac{\partial}{\partial x} (e^{2 x})

Apply the chain rule:

e^{2 x} \frac{\partial}{\partial x} (2 x)

= e^{2 x} \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (2 x) = 2

= cos (3 y) e^{2 x} \cdot 2

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What is (\partial)/(\partial x)(e^{2x}cos(3y)) ?
The answer to (\partial)/(\partial x)(e^{2x}cos(3y)) is cos(3y)e^{2x}*2