What is the derivative of (c^6-x^6/(c^6+x^6)) ?

The derivative of (c^6-x^6/(c^6+x^6)) is -(12c^6x^5)/((c^6+x^6)^2)

What is the first derivative of (c^6-x^6/(c^6+x^6)) ?

The first derivative of (c^6-x^6/(c^6+x^6)) is -(12c^6x^5)/((c^6+x^6)^2)

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\frac{d}{d x} (\frac{c ^{6} - x ^{6}}{c ^{6} + x ^{6}})

- \frac{12 c ^{6} x ^{5}}{( c ^{6} + x ^{6} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{c ^{6} - x ^{6}}{c ^{6} + x ^{6}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( c ^{6} - x ^{6} ) ( c ^{6} + x ^{6} ) - \frac{d}{d x} ( c ^{6} + x ^{6} ) ( c ^{6} - x ^{6} )}{( c ^{6} + x ^{6} ) ^{2}}

\frac{d}{d x} (c^{6} - x^{6}) = - 6 x^{5}

\frac{d}{d x} (c^{6} + x^{6}) = 6 x^{5}

= \frac{( - 6 x ^{5} ) ( c ^{6} + x ^{6} ) - 6 x ^{5} ( c ^{6} - x ^{6} )}{( c ^{6} + x ^{6} ) ^{2}}

Simplify

\frac{( - 6 x ^{5} ) ( c ^{6} + x ^{6} ) - 6 x ^{5} ( c ^{6} - x ^{6} )}{( c ^{6} + x ^{6} ) ^{2}} : - \frac{12 c ^{6} x ^{5}}{( c ^{6} + x ^{6} ) ^{2}}

= - \frac{12 c ^{6} x ^{5}}{( c ^{6} + x ^{6} ) ^{2}}

n = 1 \sum \infty (\frac{1}{n + 1})^{2}

\int_{0}^{3} (2 x - x^{2})^{5} (1 - x) d x

\frac{d}{d x} (cos (x + 2 y))

\int_{0}^{2} π (x^{3} - 8)^{2} d x

\frac{d}{d x} (3 e^{3 x} \cdot cos (2 x))

What is the derivative of (c^6-x^6/(c^6+x^6)) ?
The derivative of (c^6-x^6/(c^6+x^6)) is -(12c^6x^5)/((c^6+x^6)^2)
What is the first derivative of (c^6-x^6/(c^6+x^6)) ?
The first derivative of (c^6-x^6/(c^6+x^6)) is -(12c^6x^5)/((c^6+x^6)^2)