Find the Derivative - d/dx ((x^2-2)^(3/2))/3

Problem

d()/d(x)((x2−2)(3/2))/3

Solution

1. Identify the constant factor and move it outside the derivative to simplify the expression.

1/3d(x2−2)/d(x)

2. Apply the power rule and the chain rule to the expression (x2−2)(3/2)

1/3⋅3/2*(x2−2)(1/2)⋅d(x2−2)/d(x)

3. Differentiate the inner function x2−2 with respect to x

1/3⋅3/2*(x2−2)(1/2)⋅2*x

4. Simplify the expression by canceling the constants 1/3 and 3 and the 2 in the denominator with the 2*x

x*(x2−2)(1/2)

5. Rewrite the expression using radical notation if desired.

x√(,x2−2)

Final Answer

d()/d(x)((x2−2)(3/2))/3=x√(,x2−2)

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