What is (\partial)/(\partial x)(x/(x^7-y^5)) ?

The answer to (\partial)/(\partial x)(x/(x^7-y^5)) is (-6x^7-y^5)/((x^7-y^5)^2)

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(\partial)/(\partial x)(x/(x^7-y^5))

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{5}})

\frac{- 6 x ^{7} - y ^{5}}{( x ^{7} - y ^{5} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{5}})

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 ^{5} ) - \frac{\partial}{\partial x} ( x ^{7} - y ^{5} ) x}{( x ^{7} - y ^{5} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{7} - y^{5}) = 7 x^{6}

= \frac{1 \cdot ( x ^{7} - y ^{5} ) - 7 x ^{6} x}{( x ^{7} - y ^{5} ) ^{2}}

1 \cdot (x^{7} - y^{5}) - 7 x^{6} x = - 6 x^{7} - y^{5}

= \frac{- 6 x ^{7} - y ^{5}}{( x ^{7} - y ^{5} ) ^{2}}

x \to 0 + lim (e^{3 x l n (x)})

(arctan (6 x))^{2}

\frac{d y}{d x} = - \frac{x}{y}, y (4) = 3

\frac{d y}{d x} = e^{8 x} + 13 y

x \to \frac{π}{3} lim (\frac{2 cos ^{2} ( x ) + 3 cos ( x ) - 2}{2 cos ( x ) - 1})

What is (\partial)/(\partial x)(x/(x^7-y^5)) ?
The answer to (\partial)/(\partial x)(x/(x^7-y^5)) is (-6x^7-y^5)/((x^7-y^5)^2)