Find the Derivative of the Function $y=8 \cos ^{-1}\left(\sin ^{-1} t\right)$

question 83

Multiple Choice

Find the derivative of the function. $y=8 \cos ^{-1}\left(\sin ^{-1} t\right)$

• A) \(y^{\prime}=-\frac{8}{\sqrt{1-\left(\sin ^{-1}(t)\right)^{2}}}\)
• B) \(y^{\prime}=-\frac{8}{\sqrt{\left(1-t^{2}\right)\left(1-\sin ^{-1}(t)\right)}}\)
• C) \(y^{\prime}=-\frac{8}{\sqrt{\left(1+t^{2}\right)\left(1+\left(\sin ^{-1}(t)\right)^{2}\right)}}\)
• D) \(y^{\prime}=-\frac{8}{\sqrt{\left(1-t^{2}\right)\left(1-\left(\sin ^{-1}(t)\right)^{2}\right)}}\)
• E) \(y^{\prime}=-\frac{8}{\sqrt{\left(1-t^{2}\right)}}\)

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Definitions:

Unconditioned Stimulus

A stimulus that naturally and automatically triggers a response without the need for prior learning.

Conditioned Response

A learned reaction to a specific stimulus as a result of consistent pairing with another stimulus.

Systematic Desensitization

A behavioral therapy technique used to reduce anxiety or fear through gradual exposure to the feared object or situation paired with relaxation exercises.

Relaxation Training

Techniques designed to teach individuals how to reduce stress and tension in the body, promoting a state of calm.