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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 - sin (x)) = - cos (x)

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

Simplify

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

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

x d x + \frac{1}{y} d y = 0

\int (e^{- x} - e^{5}) (e^{x} + e^{- 2}) d x

\int x 4^{3 x^{2}} d x

(x y + 2 x + y + 2) d x + (x^{2} + 2 x) d y = 0

\int \frac{x + 1}{x ^{2} - 2 x + 1} d x

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