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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{2}{x ^{7}}

e^{\frac{- x}{2}}

\frac{\partial}{\partial x} (x^{2} + sin (y) - 0.4)

(2 x e^{x} - y + 6 x^{2}) d x - x d y = 0

(7, - 1), (0, - 6)

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