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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

= \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}}}

f (x) = 8 x + 2 x^{2} - x^{3}, g (x) = 0

\int \frac{sec ( y )}{co tan ( y )} d y

2 x y y^{^{'}} = y^{2} - x^{2}

h \to 0 lim (- 2 x - h + 4)

\int z z^{2} - 5 d z

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