What is (\partial)/(\partial x)(e^{6y}cos(-6x)) ?

The answer to (\partial)/(\partial x)(e^{6y}cos(-6x)) is -6e^{6y}sin(6x)

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(\partial)/(\partial x)(e^{6y}cos(-6x))

\frac{\partial}{\partial x} (e^{6 y} cos (- 6 x))

- 6 e^{6 y} sin (6 x)

Solution steps

\frac{\partial}{\partial x} (e^{6 y} cos (- 6 x))

Simplify

e^{6 y} cos (- 6 x) : e^{6 y} cos (6 x)

= \frac{\partial}{\partial x} (e^{6 y} cos (6 x))

Treat

y

as a constant

Take the constant out:

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

= e^{6 y} \frac{\partial}{\partial x} (cos (6 x))

Apply the chain rule:

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

= - sin (6 x) \frac{\partial}{\partial x} (6 x)

\frac{\partial}{\partial x} (6 x) = 6

= e^{6 y} (- sin (6 x) \cdot 6)

Simplify

= - 6 e^{6 y} sin (6 x)

\frac{d y}{d x} = (\frac{1 + 2 y ^{2}}{y sin ( x )})

\frac{d y}{d x} = \frac{x ( y - 2 )}{x ^{2} + 4}, y (1) = 5

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{2}})

x \to 1 lim (\frac{x}{x - 3})

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

What is (\partial)/(\partial x)(e^{6y}cos(-6x)) ?
The answer to (\partial)/(\partial x)(e^{6y}cos(-6x)) is -6e^{6y}sin(6x)