Find the Derivative - d/dx y=(3 square root of x)/x

Problem

d()/d(x)(3√(,x))/x

Solution

1. Simplify the expression by rewriting the square root as a fractional power and using the laws of exponents.

(3√(,x))/x=(3*x(1/2))/(x1)

2. Subtract the exponents to combine the terms into a single power of x

3*x(1/2−1)=3*x(−1/2)

3. Apply the power rule for differentiation, which states that d(xn)/d(x)=n*x(n−1)

(d(3)*x(−1/2))/d(x)=3⋅(−1/2)*x(−1/2−1)

4. Simplify the coefficient and the exponent.

−3/2*x(−3/2)

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

−3/(2*x(3/2))=−3/(2*x√(,x))

Final Answer

d()/d(x)(3√(,x))/x=−3/(2*x√(,x))

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