What is the derivative of (x^{1/3}-1^3) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x y^{^{'}} = y + 3 x^{2} sin (x), y (π) = 0

\int_{2}^{4} \frac{1}{x ^{2} - 25} d x

x \to 0 lim ((4 x)^{7 x})

- 2 x^{2} + x, - 2, 1

n = 0 \sum \infty \frac{1}{2}

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