Find the Derivative - d/dx y = natural log of x natural log of x

Problem

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

Solution

1. Rewrite the expression using exponents to simplify the differentiation process.

ln(x)*ln(x)=(ln(x))2

2. Apply the power rule and the chain rule to the expression.

d(un)/d(x)=n*u(n−1)d(u)/d(x)

3. Identify the inner function and its derivative.

u=ln(x)

d(u)/d(x)=1/x

4. Substitute the components into the chain rule formula.

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

5. Multiply the terms to find the final derivative.

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

Final Answer

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

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