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

Problem

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

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is arcsin(u) and the inner function is u=2*x

2. Apply the formula for the derivative of the inverse sine function, which is d(arcsin(u))/d(u)=1/√(,1−u2)

3. Differentiate the inner function u=2*x with respect to x which gives d(u)/d(x)=2

4. Multiply the derivative of the outer function by the derivative of the inner function according to the Chain Rule.

d(arcsin(2*x))/d(x)=1/√(,1−(2*x)2)⋅2

5. Simplify the expression by squaring the term inside the square root and moving the constant to the numerator.

d(arcsin(2*x))/d(x)=2/√(,1−4*x2)

Final Answer

d(arcsin(2*x))/d(x)=2/√(,1−4*x2)

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