What is (\partial}{\partial x}(\frac{3y)/x) ?

The answer to (\partial}{\partial x}(\frac{3y)/x) is -(3y)/(x^2)

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(\partial}{\partial x}(\frac{3y)/x)

\frac{\partial}{\partial x} (\frac{3 y}{x})

- \frac{3 y}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{3 y}{x})

Treat

y

as a constant

Take the constant out:

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

= 3 y \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= 3 y \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= 3 y (- 1 \cdot x^{- 1 - 1})

Simplify

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

= - \frac{3 y}{x ^{2}}

y^{^{''}} + 6 y^{^{'}} + 25 = 0

y^{^{''}} + 6 y^{^{'}} + 10 y = 5 t - 2

\int_{1}^{3} π (\frac{1}{x} + 1)^{2} d x

y^{2} e^{t} + (e^{t} + 2) y^{^{'}} = 0

\int \frac{x ^{2} + 4 x - 5}{( x ^{2} - 9 ) ( x + 1 )} d x

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