What is the d/(dy)(xcos(y)) ?

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

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

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

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

- x sin (y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= x (- sin (y))

Simplify

= - x sin (y)

\int \frac{x ^{3} + x ^{2}}{x ^{2} + 5 x + 6} d x

\frac{d}{d x} (\frac{x ^{2} e ^{x}}{x ^{2} + e ^{x}})

y^{^{''}} - 4 y^{^{'}} + 4 y^{^{'}} = 0

\int cos^{3} (\frac{x}{12}) d x

x \to 4 + lim (\frac{x - 4}{x - 4})