Find the derivative of the function. $$y = 3 \sin ^ { - 1 } \left( x ^ { 2 } \right)$$
A)
$y ^ { t } = \frac { 6 x } { \sqrt { 1 + x ^ { 4 } } }$
B)
$y ^ {t } = \frac { x } { \sqrt { 1 - x ^ { 2 } } }$
C)
$y ^ { t } = \frac { 6 x } { \sqrt { 1 - x ^ { 4 } } }$
D)
$y ^ { t } = \frac { 6 x } { \sqrt { 1 - x ^ { 2 } } }$
E) None of these

Question

Quizplus · Accepted Answer

To find the derivative of $y = 3 \sin ^ { - 1 } \left( x ^ { 2 } \right)$, we use the chain rule. The derivative of $\sin^{-1}(u)$ with respect to $u$ is $\frac{1}{\sqrt{1-u^2}}$. Here, $u = x^2$, so $du/dx = 2x$. Applying the chain rule, we get $y' = 3 \cdot \frac{1}{\sqrt{1-(x^2)^2}} \cdot 2x = \frac{6x}{\sqrt{1-x^4}}$.

Find the Derivative of the Function y=3sin⁡−1(x2)y = 3 \sin ^ { - 1 } \left( x ^ { 2 } \right)y=3sin−1(x2)

Find the Derivative of the Function $y = 3 \sin ^ { - 1 } \left( x ^ { 2 } \right)$