What is (\partial)/(\partial x)(1/2 yx^2) ?

The answer to (\partial)/(\partial x)(1/2 yx^2) is yx

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(\partial)/(\partial x)(1/2 yx^2)

\frac{\partial}{\partial x} (\frac{1}{2} y x^{2})

y x

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2} y x^{2})

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= y x

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{\frac{1}{3}})

f (x) = arcsin (5 x)

x \to 1 lim (\frac{- 1}{x - 1})

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

\frac{d}{d x} (\frac{1}{x ^{7} + 2})

What is (\partial)/(\partial x)(1/2 yx^2) ?
The answer to (\partial)/(\partial x)(1/2 yx^2) is yx