What is (\partial)/(\partial x)(-6ysin(3x)) ?

The answer to (\partial)/(\partial x)(-6ysin(3x)) is -18ycos(3x)

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(\partial)/(\partial x)(-6ysin(3x))

\frac{\partial}{\partial x} (- 6 y sin (3 x))

- 18 y cos (3 x)

Solution steps

\frac{\partial}{\partial x} (- 6 y sin (3 x))

Treat

y

as a constant

Take the constant out:

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

= - 6 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

= - 6 y cos (3 x) \cdot 3

Simplify

= - 18 y cos (3 x)

\int \frac{1}{x 4 x ^{2} + 25} d x

y = 3 cos (x) sin (x)

8 arcsin (e^{\frac{x}{2}})

\frac{s}{s ^{2} ( s ^{2} + 1 )}

\frac{d}{d t} (e^{2 t})

What is (\partial)/(\partial x)(-6ysin(3x)) ?
The answer to (\partial)/(\partial x)(-6ysin(3x)) is -18ycos(3x)