What is (\partial)/(\partial x)((2y)/(x^2)) ?

The answer to (\partial)/(\partial x)((2y)/(x^2)) is -(4y)/(x^3)

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(\partial)/(\partial x)((2y)/(x^2))

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

- \frac{4 y}{x ^{3}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= 2 y (- 2 x^{- 2 - 1})

Simplify

2 y (- 2 x^{- 2 - 1}) : - \frac{4 y}{x ^{3}}

= - \frac{4 y}{x ^{3}}

f (y) = 6 x^{2} ln (x^{2})

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

\frac{\partial}{\partial x} (e^{- x a})

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = a, y^{^{'}} (0) = - 5

\int (t^{2} - 6)^{2} d t

What is (\partial)/(\partial x)((2y)/(x^2)) ?
The answer to (\partial)/(\partial x)((2y)/(x^2)) is -(4y)/(x^3)