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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

\frac{d}{d x} (c_{1} e^{x} + c_{2} x e^{x})

n = 0 \sum \infty \frac{1}{1 0 ^{n}}

y^{^{'}} + 7 y = t + e^{- 2 t}

x \to 0 + lim (x^{3} + 3 x + 2)

\int \frac{2}{x ^{2} + 2 x + 2} d x

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