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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

cos (3 y) \frac{\partial}{\partial y} (3 y)

= cos (3 y) \frac{\partial}{\partial y} (3 y)

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

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

f (x) = \frac{- 2 x}{x ^{2} + 1}

n = 1 \sum \infty \frac{2 n + 1}{4 ^{n}}

x \to 3 lim (\frac{( - 4 ) ( 0 )}{4})

\frac{x ^{7} + 2}{x ^{7}}

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