Derivative of \( \displaystyle \operatorname{asin}{\left(2 x - 1 \right)} \)

Problem 2.560 · medium

1. \[ \frac{d}{d x} \operatorname{asin}{\left(2 x - 1 \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{\frac{d}{d x} \left(2 x - 1\right)}{\sqrt{1 - \left(2 x - 1\right)^{2}}} \]
   inverse-trigApply the derivative rule for arcsine.✓ Proved
3. \[ = \frac{2}{\sqrt{1 - \left(2 x - 1\right)^{2}}} \]
   derivative algebraDifferentiate the inner linear function. Combine the terms into a single fraction.✓ Proved
4. \[ = \frac{2}{\sqrt{- 4 x^{2} + 4 x}} \]
   algebra algebra algebraExpand the squared term inside the square root. Simplify the expression inside the square root. Factor out the constant 4.✓ Proved
5. \[ = \frac{1}{\sqrt{- x^{2} + x}} \]
   algebra simplifyTake the square root of 4. Simplify the fraction.✓ Proved