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

The answer to (\partial)/(\partial x)(-6e^{6y}sin(6x)) is -36e^{6y}cos(6x)

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= - 36 e^{6 y} cos (6 x)

\frac{d y}{d x} = \frac{( x - 2 )}{y - 2}

\int ln (x + 2) d x

5 y^{^{'}} - y = e^{- t} + 3 t

\int \frac{( 9 sin ^{3} ( x ) )}{cos ( x )} d x

x \to \infty lim (\frac{1}{5 x})

What is (\partial)/(\partial x)(-6e^{6y}sin(6x)) ?
The answer to (\partial)/(\partial x)(-6e^{6y}sin(6x)) is -36e^{6y}cos(6x)