Find the Derivative - d/du

Problem

d()/d(u)*(u−√(,u))*(u+√(,u))

Solution

1. Identify the expression as a difference of squares in the form (a−b)*(a+b) where a=u and b=√(,u)

2. Simplify the expression by multiplying the binomials before differentiating.

(u−√(,u))*(u+√(,u))=u2−(√(,u))2

3. Simplify the result of the multiplication further.

u2−u

4. Apply the power rule for differentiation, which states d(un)/d(u)=n*u(n−1) to each term.

d(u2)/d(u)=2*u

d(u)/d(u)=1

5. Combine the derivatives of the individual terms.

2*u−1

Final Answer

d()/d(u)*(u−√(,u))*(u+√(,u))=2*u−1

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