Learn how to find the derivative of arcsin x. The derivative is d/dx[arcsin x].
Below is the graph of f(x) = arcsin x and its derivative f'(x). Notice how the original function and derivative relate to each other.
Original Function:
Derivative:
This derivative represents the rate of change of the original function. The calculation follows standard differentiation rules as shown in the step-by-step solution below.
arcsin x is the inverse of the sine function. The Power Rule is used because the function has a form similar to that of other basic trigonometric functions, allowing us to differentiate it systematically.
💡 Why this works: The inverse sine function, arcsin x, is differentiated using the chain rule and its specific trigonometric structure. The Power Rule helps by simplifying the process of differentiation.
To find the derivative of arcsin x, we apply the Power Rule, recognizing that it involves the square root of a polynomial expression inside a function.
💡 Why this works: The derivative of arcsin x involves applying the chain rule. This gives us the final derivative: d/dx[arcsin x] = 1 / √(1 - x²).
Once the Power Rule is applied and the chain rule is considered, we simplify the expression to get the final derivative.
💡 Why this works: After applying the appropriate rules, we arrive at the simplified form of the derivative: d/dx[arcsin x] = 1 / √(1 - x²), which accurately describes how arcsin x behaves for values of x within its domain.
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❌ Common Mistake:
Not simplifying the final answer
✅ Correct Approach:
Always simplify your derivative to its most reduced form
Double-check your work by comparing your steps with our solution. Use our calculator to verify each step of the differentiation process.
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