Find the Derivative - d/dx square root of x^2-1

Problem

d(√(,x2−1))/d(x)

Solution

1. Rewrite the square root as a power to make it easier to differentiate using the power rule.

√(,x2−1)=(x2−1)(1/2)

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

d(x2−1)/d(x)=1/2*(x2−1)(−1/2)⋅d(x2−1)/d(x)

3. Differentiate the inner function x2−1 with respect to x

d(x2−1)/d(x)=2*x

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

1/2*(x2−1)(−1/2)⋅2*x

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

x/((x2−1)(1/2))

6. Convert the fractional exponent back into radical form.

x/√(,x2−1)

Final Answer

d(√(,x2−1))/d(x)=x/√(,x2−1)

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