Find the Derivative - d/dx y=(9 square root of x)/x

Problem

d()/d(x)(9√(,x))/x

Solution

1. Simplify the expression before differentiating by using the properties of exponents.

(9√(,x))/x=(9*x^(1/2))/(x^1)

2. Subtract the exponents using the rule (x^a)/(x^b)=x^(a−b)

9*x^(1/2−1)=9*x^(−1/2)

3. Apply the power rule for derivatives, which states d()/d(x)*a*x^n=n⋅a*x^(n−1)

d()/d(x)*9*x^(−1/2)=−1/2⋅9*x^(−1/2−1)

4. Simplify the resulting expression.

−9/2*x^(−3/2)

5. Rewrite the expression using positive exponents and radical notation.

−9/(2*x^(3/2))=−9/(2*x√(,x))

Final Answer

d()/d(x)(9√(,x))/x=−9/(2*x√(,x))

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