What is (\partial)/(\partial y)((5x)/(6y)) ?

The answer to (\partial)/(\partial y)((5x)/(6y)) is -(5x)/(6y^2)

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(\partial)/(\partial y)((5x)/(6y))

\frac{\partial}{\partial y} (\frac{5 x}{6 y})

- \frac{5 x}{6 y ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{5 x}{6 y})

Treat

x

as a constant

Take the constant out:

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

= \frac{5 x}{6} \frac{\partial}{\partial y} (\frac{1}{y})

Apply exponent rule:

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

= \frac{5 x}{6} \frac{\partial}{\partial y} (y^{- 1})

Apply the Power Rule:

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

= \frac{5 x}{6} (- 1 \cdot y^{- 1 - 1})

Simplify

\frac{5 x}{6} (- 1 \cdot y^{- 1 - 1}) : - \frac{5 x}{6 y ^{2}}

= - \frac{5 x}{6 y ^{2}}

(cot (x))^{^{'}}

\frac{\partial}{\partial x} (tan (3 x - 4 y))

\int \frac{3}{u ^{2} + 2} d u

f (x) = (2 x - x^{2})^{3}

\frac{d}{d x} (sec^{4} (x) - tan^{4} (x))

What is (\partial)/(\partial y)((5x)/(6y)) ?
The answer to (\partial)/(\partial y)((5x)/(6y)) is -(5x)/(6y^2)