What is (\partial)/(\partial x)(3ysin(-3x)) ?

The answer to (\partial)/(\partial x)(3ysin(-3x)) is -9ycos(3x)

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(\partial)/(\partial x)(3ysin(-3x))

\frac{\partial}{\partial x} (3 y sin (- 3 x))

- 9 y cos (3 x)

Solution steps

\frac{\partial}{\partial x} (3 y sin (- 3 x))

Simplify

3 y sin (- 3 x) : - 3 y sin (3 x)

= \frac{\partial}{\partial x} (- 3 y sin (3 x))

Treat

y

as a constant

Take the constant out:

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

= - 3 y \frac{\partial}{\partial x} (sin (3 x))

Apply the chain rule:

cos (3 x) \frac{\partial}{\partial x} (3 x)

= cos (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= - 3 y cos (3 x) \cdot 3

Simplify

= - 9 y cos (3 x)

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What is (\partial)/(\partial x)(3ysin(-3x)) ?
The answer to (\partial)/(\partial x)(3ysin(-3x)) is -9ycos(3x)