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)=a^2−b^2

2. Simplify the function h(u) by expanding the product before differentiating.

h(u)=u^2−(√(,u))^2

3. Simplify the expression further by evaluating the square of the square root.

h(u)=u^2−u

4. Apply the power rule d(u^n)/d(u)=n*u^(n−1) to each term of the simplified function.

d(h(u))/d(u)=d(u^2)/d(u)−d(u)/d(u)

5. Calculate the derivative of each term.

d(h(u))/d(u)=2*u−1

Final Answer

d()/d(u)*(u−√(,u))*(u+√(,u))=2*u−1

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