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)}

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\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}}}

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)}