$\text { Find the derivative of the function } h ( t ) = 2 \sin ( \arccos t ) \text {. }$
A) $\frac { 2 } { \sqrt { 1 - t ^ { 2 } } }$
B) $2 t \sqrt { 1 - t ^ { 2 } }$
C) $- \frac { 2 t } { \sqrt { 1 - t ^ { 2 } } }$
D) $\frac { t } { \sqrt { 1 + t ^ { 2 } } }$
E) $2 t \sqrt { 1 + t ^ { 2 } }$

Question

$\text { Find the derivative of the function } h ( t ) = 2 \sin ( \arccos t ) \text {. }$ 
A) $\frac { 2 } { \sqrt { 1 - t ^ { 2 } } }$
B) $2 t \sqrt { 1 - t ^ { 2 } }$
C) $- \frac { 2 t } { \sqrt { 1 - t ^ { 2 } } }$
D) $\frac { t } { \sqrt { 1 + t ^ { 2 } } }$
E) $2 t \sqrt { 1 + t ^ { 2 } }$

Quizplus · Accepted Answer

To find the derivative of $h(t) = 2\sin(\arccos(t))$, we use the chain rule and the fact that $\sin(\arccos(t)) = \sqrt{1-t^2}$. Differentiating $2\sqrt{1-t^2}$ with respect to $t$ gives $-\frac{2t}{\sqrt{1-t^2}}$, which corresponds to choice C.

Find the derivative of the function h(t)=2sin⁡(arccos⁡t). \text { Find the derivative of the function } h ( t ) = 2 \sin ( \arccos t ) \text {. } Find the derivative of the function h(t)=2sin(arccost).

$\text { Find the derivative of the function } h ( t ) = 2 \sin ( \arccos t ) \text {. }$