Find the Derivative - d/dx (x^2-1)^2

Problem

d(x2−1)/d(x)

Solution

1. Identify the rule needed to differentiate the expression, which is the power rule combined with the chain rule.

2. Apply the power rule to the outer function by bringing the exponent 2 to the front and decreasing the power by 1

2*(x2−1)(2−1)

3. Apply the chain rule by multiplying the result by the derivative of the inner function x2−1

2*(x2−1)⋅(d(x2)−1)/d(x)

4. Differentiate the inner function x2−1 to get 2*x

2*(x2−1)⋅2*x

5. Simplify the expression by multiplying the terms together.

4*x*(x2−1)

Final Answer

d(x2−1)/d(x)=4*x3−4*x

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