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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

tangent of f(x)=sqrt(x),(49,7)tangent of

f (x) = x, (49, 7)

derivative of (4x)/(5-cot(x))derivative of

\frac{4 x}{5 - cot ( x )}

(\partial)/(\partial y)(x^{y/z})

\frac{\partial}{\partial y} (x^{\frac{y}{z}})

(\partial)/(\partial x)(x^3y^2z)

\frac{\partial}{\partial x} (x^{3} y^{2} z)

integral of (x^2+2)/(x(x-1)^3)

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

Frequently Asked Questions (FAQ)

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