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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (1 - x^{2})^{- \frac{1}{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d y}{d x} = \frac{x}{4 y}

\frac{x ^{2} + 1}{x ^{2} - 1}

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

\int 3 x e^{\frac{2 x}{3}} d x

\frac{d}{d x} (4 - 7 x)

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