What is (\partial)/(\partial x)(x/(x^5-y^3)) ?

The answer to (\partial)/(\partial x)(x/(x^5-y^3)) is (-4x^5-y^3)/((x^5-y^3)^2)

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(\partial)/(\partial x)(x/(x^5-y^3))

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{3}})

\frac{- 4 x ^{5} - y ^{3}}{( x ^{5} - y ^{3} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{3}})

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( x ) ( x ^{5} - y ^{3} ) - \frac{\partial}{\partial x} ( x ^{5} - y ^{3} ) x}{( x ^{5} - y ^{3} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{5} - y^{3}) = 5 x^{4}

= \frac{1 \cdot ( x ^{5} - y ^{3} ) - 5 x ^{4} x}{( x ^{5} - y ^{3} ) ^{2}}

1 \cdot (x^{5} - y^{3}) - 5 x^{4} x = - 4 x^{5} - y^{3}

= \frac{- 4 x ^{5} - y ^{3}}{( x ^{5} - y ^{3} ) ^{2}}

\frac{d}{d x} (- 2 x - 1)

\int \frac{1}{( 9 + x ^{2} ) ^{\frac{3}{2}}} d x

\frac{x}{8 + x}

\frac{e ^{- 3 s}}{s ^{2}}

(t + 1)^{2}

What is (\partial)/(\partial x)(x/(x^5-y^3)) ?
The answer to (\partial)/(\partial x)(x/(x^5-y^3)) is (-4x^5-y^3)/((x^5-y^3)^2)