What is (\partial)/(\partial x)(xysin(x)+ye^{xy}) ?

The answer to (\partial)/(\partial x)(xysin(x)+ye^{xy}) is y(sin(x)+xcos(x))+y^2e^{yx}

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(\partial)/(\partial x)(xysin(x)+ye^{xy})

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

y (sin (x) + x cos (x)) + y^{2} e^{y x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= y (sin (x) + x cos (x)) + y^{2} e^{y x}

f (x) = \frac{5 x - 7}{6 x - 9}

\int e^{x} 29 + e^{x} d x

\int x e^{t x} d x

\frac{d y}{d t} = 7 t e^{- y}, y (0) = 3

\frac{d}{d y} (7 y)

What is (\partial)/(\partial x)(xysin(x)+ye^{xy}) ?
The answer to (\partial)/(\partial x)(xysin(x)+ye^{xy}) is y(sin(x)+xcos(x))+y^2e^{yx}