What is the derivative of (c^9-x^9/(c^9+x^9)) ?

The derivative of (c^9-x^9/(c^9+x^9)) is -(18c^9x^8)/((c^9+x^9)^2)

What is the first derivative of (c^9-x^9/(c^9+x^9)) ?

The first derivative of (c^9-x^9/(c^9+x^9)) is -(18c^9x^8)/((c^9+x^9)^2)

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\frac{d}{d x} (\frac{c ^{9} - x ^{9}}{c ^{9} + x ^{9}})

- \frac{18 c ^{9} x ^{8}}{( c ^{9} + x ^{9} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{c ^{9} - x ^{9}}{c ^{9} + x ^{9}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( c ^{9} - x ^{9} ) ( c ^{9} + x ^{9} ) - \frac{d}{d x} ( c ^{9} + x ^{9} ) ( c ^{9} - x ^{9} )}{( c ^{9} + x ^{9} ) ^{2}}

\frac{d}{d x} (c^{9} - x^{9}) = - 9 x^{8}

\frac{d}{d x} (c^{9} + x^{9}) = 9 x^{8}

= \frac{( - 9 x ^{8} ) ( c ^{9} + x ^{9} ) - 9 x ^{8} ( c ^{9} - x ^{9} )}{( c ^{9} + x ^{9} ) ^{2}}

Simplify

\frac{( - 9 x ^{8} ) ( c ^{9} + x ^{9} ) - 9 x ^{8} ( c ^{9} - x ^{9} )}{( c ^{9} + x ^{9} ) ^{2}} : - \frac{18 c ^{9} x ^{8}}{( c ^{9} + x ^{9} ) ^{2}}

= - \frac{18 c ^{9} x ^{8}}{( c ^{9} + x ^{9} ) ^{2}}

What is the derivative of (c^9-x^9/(c^9+x^9)) ?
The derivative of (c^9-x^9/(c^9+x^9)) is -(18c^9x^8)/((c^9+x^9)^2)
What is the first derivative of (c^9-x^9/(c^9+x^9)) ?
The first derivative of (c^9-x^9/(c^9+x^9)) is -(18c^9x^8)/((c^9+x^9)^2)