Find the Derivative - d/dx arcsin(2x+1)

Problem

d(arcsin(2*x+1))/d(x)

Solution

1. Identify the outer function as arcsin(u) and the inner function as u=2*x+1

2. Apply the chain rule, which states that d(arcsin(u))/d(x)=1/√(,1−u2)⋅d(u)/d(x)

3. Differentiate the inner function u=2*x+1 with respect to x to get d(u)/d(x)=2

4. Substitute u and d(u)/d(x) into the chain rule formula.

5. Simplify the expression inside the square root by expanding (2*x+1)2=4*x2+4*x+1

6. Combine terms within the square root: 1−(4*x2+4*x+1)=−4*x2−4*x

7. Factor the denominator to simplify further if possible.

Final Answer

d(arcsin(2*x+1))/d(x)=2/√(,−4*x2−4*x)

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