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

The d/(dy)(xsqrt(y)) is x/(2sqrt(y))

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

The first d/(dy)(xsqrt(y)) is x/(2sqrt(y))

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

\frac{x}{2 y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply radical rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{x}{2 y}

x^{2} y^{^{'}} + 4 x y = \frac{sin ( 3 x )}{x ^{2}}

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

\int \frac{1}{t ^{2} 9 - t ^{2}} d t

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

\int 5 x ln (3 x) d x