What is (\partial)/(\partial x)(x/(x^5-y^4)) ?

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

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(\partial)/(\partial x)(x/(x^5-y^4))

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

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

Solution steps

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

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

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

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

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

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

\int_{- R}^{R} R^{2} - x^{2} d x

\frac{\partial}{\partial y} (x e^{- \frac{y}{x}})

\int_{1}^{\infty} \frac{5}{x ^{3}} d x

\int \frac{sec ( x ) tan ( x )}{1 + sec ( x )} d x

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

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