Find the Derivative - d/d@VAR f(x) = square root of 2x-3

Problem

d()/d(x)√(,2*x−3)

Solution

1. Rewrite the square root as a power using the rule √(,u)=u(1/2)

ƒ(x)=(2*x−3)(1/2)

2. Apply the Power Rule and the Chain Rule, which states d(un)/d(x)=n*u(n−1)⋅d(u)/d(x)

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

3. Differentiate the inner function 2*x−3 with respect to x

d(2*x−3)/d(x)=2

4. Substitute the derivative of the inner function back into the expression.

d(ƒ(x))/d(x)=1/2*(2*x−3)(−1/2)⋅2

5. Simplify the expression by canceling the constants and moving the negative exponent to the denominator.

d(ƒ(x))/d(x)=(2*x−3)(−1/2)

d(ƒ(x))/d(x)=1/√(,2*x−3)

Final Answer

d(√(,2*x−3))/d(x)=1/√(,2*x−3)

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