Find the Derivative - d/dx square root of x^2-9

Problem

d(√(,x2−9))/d(x)

Solution

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

d(x2−9)/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*(x2−9)(−1/2)⋅d(x2−9)/d(x)

3. Differentiate the inner function x2−9 with respect to x

1/2*(x2−9)(−1/2)⋅2*x

4. Simplify the expression by canceling the constant factors and moving the negative exponent to the denominator.

x/((x2−9)(1/2))

5. Convert the fractional exponent back into radical form.

x/√(,x2−9)

Final Answer

d(√(,x2−9))/d(x)=x/√(,x2−9)

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