What is (\partial)/(\partial x)(ysin(yx)) ?

The answer to (\partial)/(\partial x)(ysin(yx)) is y^2cos(yx)

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(\partial)/(\partial x)(ysin(yx))

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

y^{2} cos (y x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (y x) = y

= y cos (y x) y

Simplify

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

= y^{2} cos (y x)

n \to 100 lim ([1 + (\frac{1}{n})]^{n})

(0.2) (3.8)

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

y^{^{'}} = \frac{e ^{x + y}}{1 + e ^{x}}, y (1) = 0

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

What is (\partial)/(\partial x)(ysin(yx)) ?
The answer to (\partial)/(\partial x)(ysin(yx)) is y^2cos(yx)