What is (\partial)/(\partial x)(cos(x+6y)) ?

The answer to (\partial)/(\partial x)(cos(x+6y)) is -sin(x+6y)

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(\partial)/(\partial x)(cos(x+6y))

\frac{\partial}{\partial x} (cos (x + 6 y))

- sin (x + 6 y)

Solution steps

\frac{\partial}{\partial x} (cos (x + 6 y))

Treat

y

as a constant

Apply the chain rule:

- sin (x + 6 y) \frac{\partial}{\partial x} (x + 6 y)

= - sin (x + 6 y) \frac{\partial}{\partial x} (x + 6 y)

\frac{\partial}{\partial x} (x + 6 y) = 1

= - sin (x + 6 y) \cdot 1

Simplify

= - sin (x + 6 y)

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\frac{d y}{d x} = \frac{x + 1}{( x ^{2} + 2 x - 3 ) ^{2}}

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What is (\partial)/(\partial x)(cos(x+6y)) ?
The answer to (\partial)/(\partial x)(cos(x+6y)) is -sin(x+6y)