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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= - \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}}}

\int x^{2} 5 x + 5 d x

\int \frac{5}{33 x} x^{4} d x

t \to 0 lim (- 2 t)

\int \frac{- 7 25 x ^{2} - 9}{x ^{3}} d x

x \to 0 lim ((1 + 2 x)^{\frac{3}{x}})

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