What is the derivative of \sqrt[4]{1-x^2} ?

The derivative of \sqrt[4]{1-x^2} is -x/(2(-x^2+1)^{3/4)}

What is the first derivative of \sqrt[4]{1-x^2} ?

The first derivative of \sqrt[4]{1-x^2} is -x/(2(-x^2+1)^{3/4)}

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- \frac{x}{2 ( - x ^{2} + 1 ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( 1 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (1 - x^{2})

= \frac{1}{4 ( 1 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (1 - x^{2})

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

= \frac{1}{4 ( 1 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x)

Simplify

\frac{1}{4 ( 1 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x) : - \frac{x}{2 ( - x ^{2} + 1 ) ^{\frac{3}{4}}}

= - \frac{x}{2 ( - x ^{2} + 1 ) ^{\frac{3}{4}}}

\int e^{x} + 5 d x

\frac{\partial}{\partial x} (8 x y^{2})

\int π (e^{- x})^{2} d x

x cos (\frac{y}{x}) \frac{d y}{d x} = y cos (\frac{y}{x}) - x

What is the derivative of \sqrt[4]{1-x^2} ?
The derivative of \sqrt[4]{1-x^2} is -x/(2(-x^2+1)^{3/4)}
What is the first derivative of \sqrt[4]{1-x^2} ?
The first derivative of \sqrt[4]{1-x^2} is -x/(2(-x^2+1)^{3/4)}