Find the Derivative - d/du

Problem

d()/d(u)*(√(,3*u)+√(,5*u))

Solution

1. Rewrite the expression using fractional exponents to make differentiation easier.

√(,3*u)+√(,5*u)=(3*u)^(1/2)+(5*u)^(1/2)

2. Apply the power rule and the chain rule to each term separately.

d(3*u)/d(u)=1/2*(3*u)^(−1/2)⋅3

d(5*u)/d(u)=1/2*(5*u)^(−1/2)⋅5

3. Simplify the resulting terms by moving the negative exponents to the denominator.

3/(2√(,3*u))+5/(2√(,5*u))

4. Rationalize the denominators to simplify the constants.

3/(2√(,3)√(,u))=√(,3)/(2√(,u))

5/(2√(,5)√(,u))=√(,5)/(2√(,u))

5. Combine the terms over a common denominator.

(√(,3)+√(,5))/(2√(,u))

Final Answer

d()/d(u)*(√(,3*u)+√(,5*u))=(√(,3)+√(,5))/(2√(,u))

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