What is (\partial)/(\partial x)(-5ycos(-9x)) ?

The answer to (\partial)/(\partial x)(-5ycos(-9x)) is 45ysin(9x)

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(\partial)/(\partial x)(-5ycos(-9x))

\frac{\partial}{\partial x} (- 5 y cos (- 9 x))

45 y sin (9 x)

Solution steps

\frac{\partial}{\partial x} (- 5 y cos (- 9 x))

Simplify

- 5 y cos (- 9 x) : - 5 y cos (9 x)

= \frac{\partial}{\partial x} (- 5 y cos (9 x))

Treat

y

as a constant

Take the constant out:

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

= - 5 y \frac{\partial}{\partial x} (cos (9 x))

Apply the chain rule:

- sin (9 x) \frac{\partial}{\partial x} (9 x)

= - sin (9 x) \frac{\partial}{\partial x} (9 x)

\frac{\partial}{\partial x} (9 x) = 9

= - 5 y (- sin (9 x) \cdot 9)

Simplify

= 45 y sin (9 x)

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What is (\partial)/(\partial x)(-5ycos(-9x)) ?
The answer to (\partial)/(\partial x)(-5ycos(-9x)) is 45ysin(9x)