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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{1}{2}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

area x=y^2-2,x=6-y^2 area

x = y^{2} - 2, x = 6 - y^{2}

derivative of (4x+x^2/((2+x)^2))

\frac{d}{d x} (\frac{4 x + x ^{2}}{( 2 + x ) ^{2}})

derivative of arctan(e^xx^2)

\frac{d}{d x} (arctan (e^{x} x^{2}))

limit as x approaches 0 of 4/(sqrt(x))

x \to 0 lim (\frac{4}{x})

t y^{^{'}} - 4 y = t^{6} e^{t}

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)^{1/2)}
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)^{1/2)}