What is the d/(dy)(x^{0.5}y^{0.5}) ?

The d/(dy)(x^{0.5}y^{0.5}) is (0.5x^{1/2})/(y^{0.5)}

What is the first d/(dy)(x^{0.5}y^{0.5}) ?

The first d/(dy)(x^{0.5}y^{0.5}) is (0.5x^{1/2})/(y^{0.5)}

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\frac{d}{d y} (x^{0.5} y^{0.5})

\frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

Solution steps

\frac{d}{d y} (x^{0.5} y^{0.5})

Treat

x

as a constant

Take the constant out:

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

= x^{0.5} \frac{d}{d y} (y^{0.5})

Apply the Power Rule:

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

= x^{0.5} \cdot 0.5 y^{0.5 - 1}

Simplify

x^{\frac{1}{2}} \cdot 0.5 y^{0.5 - 1} : \frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

= \frac{0.5 x ^{\frac{1}{2}}}{y ^{0.5}}

x^{\frac{7}{9}}

f (x) = x^{2} - 7, at x = 2

\frac{d x}{d t} = 0.9 x (1900 - x)

x \to 2 - lim (\frac{x ^{2}}{x ^{2} + 4})

\frac{d y}{d x} + \frac{y}{x} = 9 x^{5} y^{2}

What is the d/(dy)(x^{0.5}y^{0.5}) ?
The d/(dy)(x^{0.5}y^{0.5}) is (0.5x^{1/2})/(y^{0.5)}
What is the first d/(dy)(x^{0.5}y^{0.5}) ?
The first d/(dy)(x^{0.5}y^{0.5}) is (0.5x^{1/2})/(y^{0.5)}