What is (\partial)/(\partial x)(-ycos(6x)) ?

The answer to (\partial)/(\partial x)(-ycos(6x)) is 6ysin(6x)

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(\partial)/(\partial x)(-ycos(6x))

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

6 y sin (6 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (6 x) = 6

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

Simplify

= 6 y sin (6 x)

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What is (\partial)/(\partial x)(-ycos(6x)) ?
The answer to (\partial)/(\partial x)(-ycos(6x)) is 6ysin(6x)