What is (\partial)/(\partial x)(x^{0.5}*y) ?

The answer to (\partial)/(\partial x)(x^{0.5}*y) is (0.5y)/(x^{0.5)}

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(\partial)/(\partial x)(x^{0.5}*y)

\frac{\partial}{\partial x} (x^{0.5} \cdot y)

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x \to 0 lim (csc (x))

\int x^{2} 4 x + 4 d x

cos (3 t) sin (2 t)

x^{2} - y^{2} = 16, (5, 3)

\int \frac{2 x ^{2} + x + 4}{x ^{3} + 4 x ^{2}} d x

What is (\partial)/(\partial x)(x^{0.5}*y) ?
The answer to (\partial)/(\partial x)(x^{0.5}*y) is (0.5y)/(x^{0.5)}