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)