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

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

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(\partial)/(\partial x)(ysin(xy))

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

y^{2} cos (y x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y cos (x y) y

Simplify

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

= y^{2} cos (y x)

\frac{d}{d x} (- \frac{36}{( 1 + 6 x ) ^{2}})

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}

\frac{\partial}{\partial y} (x e^{y} - x^{5} + y - 3)

\frac{d}{d x} (\frac{x}{x ^{2} + y ^{2} + 1})

\frac{d ^{2}}{d x ^{2}} (e^{- 3 x})

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