What is (\partial)/(\partial x)(cos(xe^{xy})) ?

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

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(\partial)/(\partial x)(cos(xe^{xy}))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

n = 1 \sum \infty \frac{4}{3 n}

x \to 0 lim (x^{4} cos (\frac{9}{x}))

t - sin (t)

ln (2 x + 1)

\int_{0}^{\frac{3}{4}} 30 x d x

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