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

The first d/(dy)(xsin(y)) is xcos(y)

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d/(dy)(xsin(y))

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

x cos (y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= x cos (y)

x \to \infty lim (\frac{5}{4})

\frac{d}{d x} (I n e^{x})

\int (x^{17} + 3 e^{x} - cos (x) + \frac{1}{x}) d x

f (x) = x^{- 6}

\frac{\partial}{\partial x} (\frac{1}{1 - \frac{5}{x}})