What is (\partial)/(\partial x)(cos(ye^{x*y})) ?

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

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(\partial)/(\partial x)(cos(ye^{x*y}))

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

- sin (y e^{x y}) y^{2} e^{y x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= - sin (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}

= - sin (y e^{x y}) y^{2} e^{y x}

\int [1 + \frac{1}{( x + 1 ) ^{2}}] d x

x \to 2 lim (4 - x)

y = \frac{x ^{5}}{3 - x ^{4}}

\frac{\partial}{\partial y} (ln (2 x^{2} + y^{2}))

x \to 4 lim (\frac{x - 4}{x ^{2} + 3 x - 28})

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