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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{( 1 - t ^{2} ) ^{\frac{1}{2}}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{2 ( 1 - t ^{2} ) ^{\frac{3}{2}}} (- 2 t) : \frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}}

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

t an g e n t f (x) = (\frac{x + 1}{x + 3})^{2}, at x = - 2

\int_{0}^{\infty} \frac{( y e ^{- \frac{y}{a}} )}{a} d y

a re a y = x^{2} - 4 x, y = 2 x + 7

\int 3 ln (x^{2} - x + 4) d x

((x - 2)^{2} (x + 4))^{^{'}}

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