$\text { Find the derivative of the function } f ( x ) = 13 \arcsin ( x - 1 ) \text {. }$
A)$\frac { 13 } { \sqrt { 1 + 2 x - x ^ { 2 } } }$
B) $\frac { 13 } { \sqrt { 2 x - x ^ { 2 } } }$
C) $\frac { 13 } { \sqrt { 1 - 4 x + x ^ { 2 } } }$
D) $\frac { 13 } { \sqrt { 2 x + x ^ { 2 } } }$
E) $\frac { 13 } { \sqrt { 4 x - x ^ { 2 } } }$

Question

$\text { Find the derivative of the function } f ( x ) = 13 \arcsin ( x - 1 ) \text {. }$ 
A)$\frac { 13 } { \sqrt { 1 + 2 x - x ^ { 2 } } }$
B) $\frac { 13 } { \sqrt { 2 x - x ^ { 2 } } }$
C) $\frac { 13 } { \sqrt { 1 - 4 x + x ^ { 2 } } }$
D) $\frac { 13 } { \sqrt { 2 x + x ^ { 2 } } }$
E) $\frac { 13 } { \sqrt { 4 x - x ^ { 2 } } }$

Quizplus · Accepted Answer

We use the chain rule and the derivative of the inverse sine function:
$$f'(x) = \frac{d}{dx}[13\arcsin(x-1)] = 13\cdot \frac{1}{\sqrt{1-(x-1)^2}} \cdot \frac{d}{dx}(x-1) = \frac{13}{\sqrt{2x-x^2}}.$$ Therefore, the answer is $\boxed{	extbf{(B)}}.$

Find the derivative of the function f(x)=13arcsin⁡(x−1). \text { Find the derivative of the function } f ( x ) = 13 \arcsin ( x - 1 ) \text {. } Find the derivative of the function f(x)=13arcsin(x−1).

$\text { Find the derivative of the function } f ( x ) = 13 \arcsin ( x - 1 ) \text {. }$