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

Problem

d(√(,3*x−2))/d(x)

Solution

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

d(3*x−2)/d(x)

2. Apply the power rule and the chain rule, which states d(un)/d(x)=n*u(n−1)⋅d(u)/d(x)

1/2*(3*x−2)(−1/2)⋅d(3*x−2)/d(x)

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

1/2*(3*x−2)(−1/2)⋅3

4. Simplify the expression by multiplying the constants and moving the negative exponent to the denominator.

3/(2*(3*x−2)(1/2))

5. Convert the fractional exponent back into radical form.

3/(2√(,3*x−2))

Final Answer

d(√(,3*x−2))/d(x)=3/(2√(,3*x−2))

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