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

The d/(dy)(sqrt(y)) is 1/(2sqrt(y))

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

The first d/(dy)(sqrt(y)) is 1/(2sqrt(y))

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

\frac{1}{2 y}

Solution steps

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

Apply radical rule:

a = a^{\frac{1}{2}}

= \frac{d}{d y} (y^{\frac{1}{2}})

Apply the Power Rule:

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

= \frac{1}{2} y^{\frac{1}{2} - 1}

Simplify

\frac{1}{2} y^{\frac{1}{2} - 1} : \frac{1}{2 y}

= \frac{1}{2 y}

\int_{0}^{1} e^{x^{3}} d x

f (x) = \frac{- 2 x}{x ^{2} + 1}, (1, - 1)

\int \frac{x}{64 x ^{2} - 1} d x

\frac{\partial}{\partial x} ((13 - x)^{80})

y (1 + x^{2}) y^{^{'}} = x (1 + y^{2})