Find the Derivative - d/dx square root of x-4

Problem

d(√(,x−4))/d(x)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to apply the power rule.

√(,x−4)=(x−4)(1/2)

2. Apply the chain rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

d(x−4)/d(x)=1/2*(x−4)(−1/2)⋅d(x−4)/d(x)

3. Differentiate the inner function x−4 with respect to x

d(x−4)/d(x)=1

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

1/2*(x−4)(−1/2)⋅1=1/(2√(,x−4))

Final Answer

d(√(,x−4))/d(x)=1/(2√(,x−4))

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