What is the first d/(dy)(ycos(x)) ?

The first d/(dy)(ycos(x)) is cos(x)

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d/(dy)(ycos(x))

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

cos (x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

\frac{d y}{d y} = 1

= cos (x) \cdot 1

Simplify

= cos (x)

\frac{\partial}{\partial x} (45 - x^{2} - y^{2})

\frac{d}{d x} (sin (2 x - 2 π))

\int \frac{1}{x ^{2} + 2 x + 5} d x

\frac{\partial}{\partial x} (ln (x^{6} + 1) + y^{2})

\frac{d}{d x} (\frac{5}{12} (3 + 5) x^{3})