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

The d/(dy)(ycos(x)y) is 2ycos(x)

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

The first d/(dy)(ycos(x)y) is 2ycos(x)

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

2 y cos (x)

Solution steps

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

Simplify

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

= \frac{d}{d y} (y^{2} cos (x))

Treat

x

as a constant

Take the constant out:

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

= cos (x) \frac{d}{d y} (y^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= cos (x) \cdot 2 y^{2 - 1}

Simplify

= 2 y cos (x)

3 x^{2} - 9

y^{^{'}} = \frac{e ^{x}}{y ^{2}}

\frac{\partial}{\partial x} (2 y + z)

\int \frac{x}{x + 4} d x

\int_{0}^{3} 5 x d x