What is (\partial)/(\partial x)(x/(x^7-y^4)) ?

The answer to (\partial)/(\partial x)(x/(x^7-y^4)) is (-6x^7-y^4)/((x^7-y^4)^2)

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(\partial)/(\partial x)(x/(x^7-y^4))

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{4}})

\frac{- 6 x ^{7} - y ^{4}}{( x ^{7} - y ^{4} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{4}})

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 ^{4} ) - \frac{\partial}{\partial x} ( x ^{7} - y ^{4} ) x}{( x ^{7} - y ^{4} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{7} - y^{4}) = 7 x^{6}

= \frac{1 \cdot ( x ^{7} - y ^{4} ) - 7 x ^{6} x}{( x ^{7} - y ^{4} ) ^{2}}

1 \cdot (x^{7} - y^{4}) - 7 x^{6} x = - 6 x^{7} - y^{4}

= \frac{- 6 x ^{7} - y ^{4}}{( x ^{7} - y ^{4} ) ^{2}}

\frac{d}{d x} (\frac{7 x ^{2}}{x ^{3}})

x \to 0 lim ((1 + x)^{\frac{7}{x}})

k (\frac{d x}{d t}) = x + 15

\int_{0}^{10} x d x

\frac{d}{d x} (\frac{( x ^{2} + 1 ) ^{2}}{( x ^{4} + 1 ) ^{4}})

What is (\partial)/(\partial x)(x/(x^7-y^4)) ?
The answer to (\partial)/(\partial x)(x/(x^7-y^4)) is (-6x^7-y^4)/((x^7-y^4)^2)