What is (\partial)/(\partial x)(sin(3x)cos(3y)) ?

The answer to (\partial)/(\partial x)(sin(3x)cos(3y)) is cos(3y)cos(3x)*3

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(\partial)/(\partial x)(sin(3x)cos(3y))

\frac{\partial}{\partial x} (sin (3 x) cos (3 y))

cos (3 y) cos (3 x) \cdot 3

Solution steps

\frac{\partial}{\partial x} (sin (3 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} (sin (3 x))

Apply the chain rule:

cos (3 x) \frac{\partial}{\partial x} (3 x)

= cos (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= cos (3 y) cos (3 x) \cdot 3

What is (\partial)/(\partial x)(sin(3x)cos(3y)) ?
The answer to (\partial)/(\partial x)(sin(3x)cos(3y)) is cos(3y)cos(3x)*3