What is (\partial)/(\partial x)(sin(x+4y)) ?

The answer to (\partial)/(\partial x)(sin(x+4y)) is cos(x+4y)

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(\partial)/(\partial x)(sin(x+4y))

\frac{\partial}{\partial x} (sin (x + 4 y))

cos (x + 4 y)

Solution steps

\frac{\partial}{\partial x} (sin (x + 4 y))

Treat

y

as a constant

Apply the chain rule:

cos (x + 4 y) \frac{\partial}{\partial x} (x + 4 y)

= cos (x + 4 y) \frac{\partial}{\partial x} (x + 4 y)

\frac{\partial}{\partial x} (x + 4 y) = 1

= cos (x + 4 y) \cdot 1

Simplify

= cos (x + 4 y)

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What is (\partial)/(\partial x)(sin(x+4y)) ?
The answer to (\partial)/(\partial x)(sin(x+4y)) is cos(x+4y)