What is (\partial)/(\partial y)(xe^xcos(y)) ?

The answer to (\partial)/(\partial y)(xe^xcos(y)) is -e^xxsin(y)

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(\partial)/(\partial y)(xe^xcos(y))

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

- e^{x} x sin (y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

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

Simplify

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

f (x) = 2 sin (2 x) - ln (3 x + 1)

\int cos (x) - cos^{2} (x) d x

\int_{2}^{4} 2 π x (- \frac{3}{2} x + 6) d x

\int \frac{x}{2} e^{- \frac{x}{2}} d x

(1 + x^{2}) \cdot \frac{d y}{d x} - \frac{4 x ^{3} y}{1 - x ^{2}} = 1

What is (\partial)/(\partial y)(xe^xcos(y)) ?
The answer to (\partial)/(\partial y)(xe^xcos(y)) is -e^xxsin(y)