What is (\partial)/(\partial x)(-3e^{3y}sin(3x)) ?

The answer to (\partial)/(\partial x)(-3e^{3y}sin(3x)) is -9e^{3y}cos(3x)

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(\partial)/(\partial x)(-3e^{3y}sin(3x))

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

- 9 e^{3 y} cos (3 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= - 3 e^{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 e^{3 y} cos (3 x) \cdot 3

Simplify

= - 9 e^{3 y} cos (3 x)

x = y^{2}, x = y + 2 [0, 4]

\frac{d}{d x} (x^{5} + x^{7} + x^{9})

x \to + 2 lim (3 x - 9)

\int x^{2} + 4 x + 13 d x

y = 5 cos (x), y = 5 sin (x)

What is (\partial)/(\partial x)(-3e^{3y}sin(3x)) ?
The answer to (\partial)/(\partial x)(-3e^{3y}sin(3x)) is -9e^{3y}cos(3x)