What is the derivative of (c^3-x^3/(c^3+x^3)) ?

The derivative of (c^3-x^3/(c^3+x^3)) is -(6c^3x^2)/((c^3+x^3)^2)

What is the first derivative of (c^3-x^3/(c^3+x^3)) ?

The first derivative of (c^3-x^3/(c^3+x^3)) is -(6c^3x^2)/((c^3+x^3)^2)

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\frac{d}{d x} (\frac{c ^{3} - x ^{3}}{c ^{3} + x ^{3}})

- \frac{6 c ^{3} x ^{2}}{( c ^{3} + x ^{3} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{c ^{3} - x ^{3}}{c ^{3} + x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( c ^{3} - x ^{3} ) ( c ^{3} + x ^{3} ) - \frac{d}{d x} ( c ^{3} + x ^{3} ) ( c ^{3} - x ^{3} )}{( c ^{3} + x ^{3} ) ^{2}}

\frac{d}{d x} (c^{3} - x^{3}) = - 3 x^{2}

\frac{d}{d x} (c^{3} + x^{3}) = 3 x^{2}

= \frac{( - 3 x ^{2} ) ( c ^{3} + x ^{3} ) - 3 x ^{2} ( c ^{3} - x ^{3} )}{( c ^{3} + x ^{3} ) ^{2}}

Simplify

\frac{( - 3 x ^{2} ) ( c ^{3} + x ^{3} ) - 3 x ^{2} ( c ^{3} - x ^{3} )}{( c ^{3} + x ^{3} ) ^{2}} : - \frac{6 c ^{3} x ^{2}}{( c ^{3} + x ^{3} ) ^{2}}

= - \frac{6 c ^{3} x ^{2}}{( c ^{3} + x ^{3} ) ^{2}}

\int \frac{8}{x x ^{2} + 2} d x

\int 5 tan^{2} (x) sec^{3} (x) d x

\int \frac{1}{x ^{2}} + \frac{1}{x x} + 5 d x

\frac{d}{d x} ((x^{4} + 2)^{2} (x^{3} + 4)^{4})

\int (e^{2 x} + e^{- 2 x}) d x

What is the derivative of (c^3-x^3/(c^3+x^3)) ?
The derivative of (c^3-x^3/(c^3+x^3)) is -(6c^3x^2)/((c^3+x^3)^2)
What is the first derivative of (c^3-x^3/(c^3+x^3)) ?
The first derivative of (c^3-x^3/(c^3+x^3)) is -(6c^3x^2)/((c^3+x^3)^2)