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Popular >

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

Solution

derivative of

(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

limit as x approaches p(x) of (f(x)-f(p))/(x-p(x))

x \to p (x) lim (\frac{f ( x ) - f ( p )}{x - p ( x )})

limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h

h \to 0 lim (\frac{sin ( \frac{π}{3} + h ) - sin ( \frac{π}{3} )}{h})

integral of 1/(49e^{-6x)+e^{6x}}

\int \frac{1}{49 e ^{- 6 x} + e ^{6 x}} d x

y^{''}+y=cos^2(t),y(0)=0,y^'(0)=0

y^{^{''}} + y = cos^{2} (t), y (0) = 0, y^{^{'}} (0) = 0

(\partial)/(\partial x)(sqrt(25+18x-y))

\frac{\partial}{\partial x} (25 + 18 x - y)

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)}