Derivative of \( \displaystyle \operatorname{asin}{\left(5 x - 1 \right)} \)

Problem 2.356 · easy

1. \[ \frac{d}{d x} \operatorname{asin}{\left(5 x - 1 \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{\frac{d}{d x} \left(5 x - 1\right)}{\sqrt{1 - \left(5 x - 1\right)^{2}}} \]
   chainApply the chain rule for the arcsine function.✓ Proved
3. \[ = \frac{- \frac{d}{d x} 1 + \frac{d}{d x} 5 x}{\sqrt{1 - \left(5 x - 1\right)^{2}}} \]
   sumDifferentiate the inner linear function.✓ Proved
4. \[ = \frac{5}{\sqrt{1 - \left(5 x - 1\right)^{2}}} \]
   derivative simplifyCompute the derivatives of 5*x and 1. Simplify the expression to the final result.✓ Proved