Find the Derivative - d/dx (x^2-4)^(2/3)

Problem

d()/d(x)*(x2−4)(2/3)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule, where the outer function is u(2/3) and the inner function is u=x2−4

2. Differentiate the outer function with respect to the inner function using the Power Rule.

2/3*(x2−4)(2/3−1)

3. Simplify the exponent of the outer derivative.

2/3*(x2−4)(−1/3)

4. Multiply by the derivative of the inner function x2−4 with respect to x

2/3*(x2−4)(−1/3)⋅d(x2−4)/d(x)

5. Calculate the derivative of the inner function, which is 2*x

2/3*(x2−4)(−1/3)⋅2*x

6. Combine the terms and simplify the expression into a single fraction.

(4*x)/(3*(x2−4)(1/3))

Final Answer

d(x2−4)/d(x)=(4*x)/(3√(3,x2−4))

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