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

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

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

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

sin (y) e^{x y} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= sin (y) e^{x y} y

x \to 0 lim (9 x^{2} - 2 x + 5)

\frac{\partial}{\partial b} (1 0^{- 2 b})

\int \frac{x ^{2}}{x ^{2} + x - 6} d x

x \to 0 lim (\frac{sin ( - x )}{x})

\frac{d}{d x} (e^{x} + cos (x))

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