Find the Derivative - d/dx x square root of 2x-3

Problem

d()/d(x)*x√(,2*x−3)

Solution

1. Identify the rule needed for the expression, which is a product of x and √(,2*x−3) We must use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the variables for the product rule where u=x and v=√(,2*x−3)=(2*x−3)(1/2)

3. Differentiate u with respect to x

d(u)/d(x)=1

4. Differentiate v using the chain rule.

d(v)/d(x)=1/2*(2*x−3)(−1/2)⋅2

d(v)/d(x)=(2*x−3)(−1/2)

d(v)/d(x)=1/√(,2*x−3)

5. Apply the product rule formula by substituting the derivatives back in.

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

6. Simplify the expression by finding a common denominator.

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

d()/d(x)*x√(,2*x−3)=(3*x−3)/√(,2*x−3)

Final Answer

d()/d(x)*x√(,2*x−3)=(3*x−3)/√(,2*x−3)

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