What is the derivative of sqrt((x^3-1/(x^3+1))) ?

The derivative of sqrt((x^3-1/(x^3+1))) is (3x^2)/(sqrt(x^3-1)(x^3+1)^{3/2)}

What is the first derivative of sqrt((x^3-1/(x^3+1))) ?

The first derivative of sqrt((x^3-1/(x^3+1))) is (3x^2)/(sqrt(x^3-1)(x^3+1)^{3/2)}

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\frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

\frac{3 x ^{2}}{x ^{3} - 1 ( x ^{3} + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

Apply the chain rule:

\frac{1}{2 \frac{x ^{3} - 1}{x ^{3} + 1}} \frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

= \frac{1}{2 \frac{x ^{3} - 1}{x ^{3} + 1}} \frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1})

\frac{d}{d x} (\frac{x ^{3} - 1}{x ^{3} + 1}) = \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

= \frac{1}{2 \frac{x ^{3} - 1}{x ^{3} + 1}} \cdot \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}}

Simplify

\frac{1}{2 \frac{x ^{3} - 1}{x ^{3} + 1}} \cdot \frac{6 x ^{2}}{( x ^{3} + 1 ) ^{2}} : \frac{3 x ^{2}}{x ^{3} - 1 ( x ^{3} + 1 ) ^{\frac{3}{2}}}

= \frac{3 x ^{2}}{x ^{3} - 1 ( x ^{3} + 1 ) ^{\frac{3}{2}}}

What is the derivative of sqrt((x^3-1/(x^3+1))) ?
The derivative of sqrt((x^3-1/(x^3+1))) is (3x^2)/(sqrt(x^3-1)(x^3+1)^{3/2)}
What is the first derivative of sqrt((x^3-1/(x^3+1))) ?
The first derivative of sqrt((x^3-1/(x^3+1))) is (3x^2)/(sqrt(x^3-1)(x^3+1)^{3/2)}