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Popular >

derivative of 1-1/(sqrt(1-x^2))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - \frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

Simplify

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

Popular Examples

(\partial)/(\partial x)((9x^2)/((x-y)^2))

\frac{\partial}{\partial x} (\frac{9 x ^{2}}{( x - y ) ^{2}})

integral from 0 to 1 of (x)

\int_{0}^{1} (x) d x

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

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

integral of cot^6(2x)

\int cot^{6} (2 x) d x

implicit (dy)/(dx),y=(arctan(9x))^2 implicit derivative

\frac{d y}{d x}, y = (arctan (9 x))^{2}

Frequently Asked Questions (FAQ)

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