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

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

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

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

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derivative of

f (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}}

\frac{d}{d x} (1 + 36 x)

\int \frac{1}{x ^{2} - 12} d x

\int \frac{x + 4}{x ^{3} + 3 x ^{2} - 10 x} d x

\int - 3 π sin (π) x d x

f (x) = - 2 sin (x), at x = \frac{3}{4} π

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