Find the Derivative - d/d@VAR f(x) = natural log of natural log of x^2

Problem

d()/d(x)*ln(ln(x2))

Solution

1. Identify the outer function as ln(u) where u=ln(x2)

2. Apply the chain rule for the natural logarithm, which states d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Differentiate the inner function u=ln(x2) by applying the chain rule again, resulting in 1/(x2)⋅d(x2)/d(x)

4. Calculate the derivative of the innermost part d(x2)/d(x)=2*x

5. Combine all parts of the chain rule together.

d(ln(ln(x2)))/d(x)=1/ln(x2)⋅1/(x2)⋅2*x

6. Simplify the expression by canceling x in the numerator and denominator.

d(ln(ln(x2)))/d(x)=(2*x)/(x2*ln(x2))

d(ln(ln(x2)))/d(x)=2/(x*ln(x2))

Final Answer

d(ln(ln(x2)))/d(x)=2/(x*ln(x2))

Want more problems? Check here!