d/dx((1-sinx)/(1+sinx))^1/2

asked by guest
on Nov 23, 2024 at 4:43 am



You asked:

Evaluate the expression: \(\frac{d}{dx}\left[\frac{{\left( \frac{1 - \sin\left( x \right)}{1 + \sin\left( x \right)} \right)}^{1}}{2}\right]\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{d}{dx}\left[\frac{{\left( \frac{1 - \sin\left( x \right)}{1 + \sin\left( x \right)} \right)}^{1}}{2}\right] = - \frac{\left(1 - \sin{\left(x \right)}\right) \cos{\left(x \right)}}{2 \left(\sin{\left(x \right)} + 1\right)^{2}} - \frac{\cos{\left(x \right)}}{2 \left(\sin{\left(x \right)} + 1\right)} \)

Expanded

\[\frac{d}{dx}\left[\frac{{\left( \frac{1 - \sin\left( x \right)}{1 + \sin\left( x \right)} \right)}^{1}}{2}\right] = \frac{d}{d x} \left(- \frac{\sin{\left(x \right)}}{2 \sin{\left(x \right)} + 2} + \frac{1}{2 \sin{\left(x \right)} + 2}\right)\]

Factored

\[\frac{d}{dx}\left[\frac{{\left( \frac{1 - \sin\left( x \right)}{1 + \sin\left( x \right)} \right)}^{1}}{2}\right] = \frac{d}{d x} \left(- \frac{\sin{\left(x \right)}}{2 \sin{\left(x \right)} + 2} + \frac{1}{2 \sin{\left(x \right)} + 2}\right)\]

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