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Find the derivatives of the given functions.$$y=3 \sin ^{-1} x^{2}$$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 3

Derivatives of the Inverse Trigonometric Functions

Derivatives

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Find the second derivative…

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we want to find the derivative dy dx for the function. Why is equal to three times the arc sine or inverse sine of X squared? This question is testing our knowledge of the different differentiation shortcuts that we picked up throughout our journey. And single variable calculus in particular, it's testing our knowledge of the newfound derivatives for inverse trig identities or for inverse trig functions. So I listed all three inverse regular this year. In particular, we need to use that DDX arc sine X is equal to one over the square root of one minus x square. We combine with this with the chain rule to solve for this derivative. So why equals three arc sine X squared is already in its most easily differential form so we can proceed differentiate. Thus we have, Do I react equals three Times. Are the General two X over one minus x squared squared square rooted or simplified? Dy dx is equal to six X divided by the square root of one minus x to the fourth.

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