What is (\partial}{\partial y}(\frac{5x)/y) ?

The answer to (\partial}{\partial y}(\frac{5x)/y) is -(5x)/(y^2)

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(\partial}{\partial y}(\frac{5x)/y)

\frac{\partial}{\partial y} (\frac{5 x}{y})

- \frac{5 x}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{5 x}{y})

Treat

x

as a constant

Take the constant out:

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

= 5 x \frac{\partial}{\partial y} (\frac{1}{y})

Apply exponent rule:

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

= 5 x \frac{\partial}{\partial y} (y^{- 1})

Apply the Power Rule:

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

= 5 x (- 1 \cdot y^{- 1 - 1})

Simplify

5 x (- 1 \cdot y^{- 1 - 1}) : - \frac{5 x}{y ^{2}}

= - \frac{5 x}{y ^{2}}

x \to - 2 lim (\frac{sin ( x )}{2 x})

\int \frac{x + 1}{x ^{2} + 2 x + 3} d x

\int \frac{e ^{3 x}}{9 + 4 e ^{6 x}} d x

\frac{2}{s ^{5}}

x \to 0 lim (\frac{( 2 + x ) ^{3} - 8}{x})

What is (\partial}{\partial y}(\frac{5x)/y) ?
The answer to (\partial}{\partial y}(\frac{5x)/y) is -(5x)/(y^2)