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

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

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

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

- 3 e^{3 y} sin (3 x)

Solution steps

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

Simplify

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

= \frac{\partial}{\partial x} (e^{3 y} cos (3 x))

Treat

y

as a constant

Take the constant out:

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

= e^{3 y} \frac{\partial}{\partial x} (cos (3 x))

Apply the chain rule:

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

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

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

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

Simplify

= - 3 e^{3 y} sin (3 x)

y = e^{x}, y = 9 - e^{x}, x = - 1, x = 1

(sin (ln (t)))^{2}

y^{^{'}} = 4 y (1 - \frac{y}{4})

x \to 0 lim (- \frac{4}{x ^{2}})

\frac{x ^{3} - 5 x ^{2} + 1}{x ^{2}}

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