Find the Derivative - d/dx y=arccos(x^2)

Problem

d()/d(x)*arccos(x2)

Solution

1. Identify the outer function as arccos(u) and the inner function as u=x2

2. Apply the chain rule, which states that d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

3. Differentiate the outer function using the rule d(arccos(u))/d(u)=−1/√(,1−u2)

4. Differentiate the inner function u=x2 to get d(u)/d(x)=2*x

5. Substitute u=x2 back into the derivative of the outer function.

6. Multiply the results of the derivatives together.

7. Simplify the expression by squaring x2 to get x4

Final Answer

d(arccos(x2))/d(x)=−(2*x)/√(,1−x4)

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