Find the Derivative - d/d@VAR

Problem

d()/d(x)*(√(,x)+5/√(,x))

Solution

1. Rewrite the expression using power notation to prepare for differentiation.

s(x)=x(1/2)+5*x(−1/2)

2. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to each term individually.

d(s(x))/d(x)=1/2*x(1/2−1)+5*(−1/2)*x(−1/2−1)

3. Simplify the exponents by performing the subtraction.

d(s(x))/d(x)=1/2*x(−1/2)−5/2*x(−3/2)

4. Convert the expression back into radical form and positive exponents for the final result.

d(s(x))/d(x)=1/(2√(,x))−5/(2√(,x3))

Final Answer

d()/d(x)*(√(,x)+5/√(,x))=1/(2√(,x))−5/(2*x√(,x))

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