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

Problem

d(arcsec(2*x))/d(x)

Solution

1. Identify the general rule for the derivative of the inverse secant function, which is d(arcsec(u))/d(x)=1/(|u|√(,u2−1))⋅d(u)/d(x)

2. Assign the inner function u=2*x

3. Calculate the derivative of the inner function, which is d(u)/d(x)=2

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

d(arcsec(2*x))/d(x)=1/(|2*x|√(,(2*x)2−1))⋅2

5. Simplify the expression by squaring the term inside the radical and canceling the common factor of 2.

d(arcsec(2*x))/d(x)=2/(2*|x|√(,4*x2−1))

d(arcsec(2*x))/d(x)=1/(|x|√(,4*x2−1))

Final Answer

d(arcsec(2*x))/d(x)=1/(|x|√(,4*x2−1))

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