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

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

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(\partial)/(\partial x)(sin(ye^{xy}))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\int e^{y x} d x

y^{^{''}} + 9 y^{^{'}} = 0, y (0) = 1

f (x) = 4 (x - 3)^{\frac{2}{3}}

\frac{d}{d x} (arctan (\frac{c}{x}))

f (x) = \frac{5 x}{x - 2}, at x = 3

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