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

Problem

d()/d(x)√(,x*(x−3))/3

Solution

1. Rewrite the expression by pulling out the constant factor and expressing the square root as a power.

d()/d(x)√(,x2−3*x)/3=1/3d()/d(x)*(x2−3*x)(1/2)

2. Apply the power rule and the chain rule to the expression inside the derivative.

d()/d(x)*(x2−3*x)(1/2)=1/2*(x2−3*x)(−1/2)⋅d(x2−3*x)/d(x)

3. Differentiate the inner function x2−3*x

d(x2−3*x)/d(x)=2*x−3

4. Combine the results and simplify the expression.

1/3⋅1/2*(x2−3*x)(−1/2)⋅(2*x−3)=(2*x−3)/(6√(,x2−3*x))

Final Answer

d()/d(x)√(,x*(x−3))/3=(2*x−3)/(6√(,x2−3*x))

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