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} 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}}

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 4

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

f (x) = x + 16, at x = 1

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

y^{^{''}} + 2 y = 3, y (0) = - 1, y (0) = 2

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)}