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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

\int t ec (2 t) d t

\frac{d}{d x} ((x + 1) \cdot (x^{2} - 1))

\frac{x ^{2} - 3}{x - 2}

\int_{- 1}^{6} (2 x + 6) - (x^{2} - 3 x) d x

\int - \frac{( csc ( x ) ) ^{2}}{cot ( x )} d x

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