What is (\partial)/(\partial x)(x/(x^7-y^6)) ?

The answer to (\partial)/(\partial x)(x/(x^7-y^6)) is (-6x^7-y^6)/((x^7-y^6)^2)

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(\partial)/(\partial x)(x/(x^7-y^6))

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{6}})

\frac{- 6 x ^{7} - y ^{6}}{( x ^{7} - y ^{6} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{6}})

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 ^{7} - y ^{6} ) - \frac{\partial}{\partial x} ( x ^{7} - y ^{6} ) x}{( x ^{7} - y ^{6} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{7} - y^{6}) = 7 x^{6}

= \frac{1 \cdot ( x ^{7} - y ^{6} ) - 7 x ^{6} x}{( x ^{7} - y ^{6} ) ^{2}}

1 \cdot (x^{7} - y^{6}) - 7 x^{6} x = - 6 x^{7} - y^{6}

= \frac{- 6 x ^{7} - y ^{6}}{( x ^{7} - y ^{6} ) ^{2}}

\int (x^{2} - 5)^{5} (2 x) d x

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

\frac{x ^{2}}{1 + x}

\int e^{\frac{- t ^{2}}{2}} d t

x \to + (- 2) - lim (\frac{1}{x ^{2} - 4})

What is (\partial)/(\partial x)(x/(x^7-y^6)) ?
The answer to (\partial)/(\partial x)(x/(x^7-y^6)) is (-6x^7-y^6)/((x^7-y^6)^2)