What is the d/(dy)(xsin(xy)) ?

The d/(dy)(xsin(xy)) is x^2cos(xy)

What is the first d/(dy)(xsin(xy)) ?

The first d/(dy)(xsin(xy)) is x^2cos(xy)

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

x^{2} cos (x y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x cos (x y) x

Simplify

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

= x^{2} cos (x y)

x \to 1 lim (\frac{1}{x - 2})

\frac{\partial}{\partial x} (3 y sin (7 y^{2} x))

\frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}}

\int_{0}^{\frac{1}{3}} \frac{4}{1 + 9 x ^{2}} d x

y = x^{3} - 2 x^{2} + 5