What is (\partial)/(\partial y)(e^{3x}sin(2y)) ?

The answer to (\partial)/(\partial y)(e^{3x}sin(2y)) is e^{3x}cos(2y)*2

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(\partial)/(\partial y)(e^{3x}sin(2y))

\frac{\partial}{\partial y} (e^{3 x} sin (2 y))

e^{3 x} cos (2 y) \cdot 2

Solution steps

\frac{\partial}{\partial y} (e^{3 x} sin (2 y))

Treat

x

as a constant

Take the constant out:

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

= e^{3 x} \frac{\partial}{\partial y} (sin (2 y))

Apply the chain rule:

cos (2 y) \frac{\partial}{\partial y} (2 y)

= cos (2 y) \frac{\partial}{\partial y} (2 y)

\frac{\partial}{\partial y} (2 y) = 2

= e^{3 x} cos (2 y) \cdot 2

cos (3 y)

\frac{d}{d x} (e^{- 5 x^{4}})

\int (x^{2} + 3) sin (x) d x

y = 3 (1)^{2} - 5 (1) + 9

\int \frac{cos ( x )}{sin ^{4} ( x ) - 16} d x

What is (\partial)/(\partial y)(e^{3x}sin(2y)) ?
The answer to (\partial)/(\partial y)(e^{3x}sin(2y)) is e^{3x}cos(2y)*2