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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

e^{x y} x sin (y) + cos (y) e^{x y}

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x y}, g = sin (y)

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

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

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

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

\int_{0}^{20} cos (π x) d x

\int ln (x - 5) d x

\frac{d}{d x} ((sin (x))^{3})

x \to 0 lim (\frac{x ^{2}}{x})

f (x) = x^{2} + 9

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