What is (\partial)/(\partial x)(sin(5x)cos(5y)) ?

The answer to (\partial)/(\partial x)(sin(5x)cos(5y)) is cos(5y)cos(5x)*5

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(\partial)/(\partial x)(sin(5x)cos(5y))

\frac{\partial}{\partial x} (sin (5 x) cos (5 y))

cos (5 y) cos (5 x) \cdot 5

Solution steps

\frac{\partial}{\partial x} (sin (5 x) cos (5 y))

Treat

y

as a constant

Take the constant out:

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

= cos (5 y) \frac{\partial}{\partial x} (sin (5 x))

Apply the chain rule:

cos (5 x) \frac{\partial}{\partial x} (5 x)

= cos (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= cos (5 y) cos (5 x) \cdot 5

What is (\partial)/(\partial x)(sin(5x)cos(5y)) ?
The answer to (\partial)/(\partial x)(sin(5x)cos(5y)) is cos(5y)cos(5x)*5