Derivative of \( \displaystyle \operatorname{asin}{\left(10 x - 6 \right)} \)

Problem 2.565 · easy

1. \[ \frac{d}{d x} \operatorname{asin}{\left(10 x - 6 \right)} \]
   derivativeStart with the derivative of the function.✓ Proved
2. \[ = \frac{\frac{d}{d x} \left(10 x - 6\right)}{\sqrt{1 - \left(10 x - 6\right)^{2}}} \]
   chainApply the chain rule for the arcsine function.✓ Proved
3. \[ = \frac{- \frac{d}{d x} 6 + \frac{d}{d x} 10 x}{\sqrt{1 - \left(10 x - 6\right)^{2}}} \]
   sumDifferentiate the terms inside the parentheses separately.✓ Proved
4. \[ = \frac{10}{\sqrt{1 - \left(10 x - 6\right)^{2}}} \]
   constant algebraThe derivative of 10*x is 10 and the derivative of 6 is 0. Simplify the expression.✓ Proved
5. \[ = \frac{10}{\sqrt{- 100 x^{2} + 120 x - 35}} \]
   algebra simplifyExpand the squared term. Simplify the expression under the square root.✓ Proved