If f(x)=sin ^{-1}(x), then what is the value of f^{prime}left(frac{sqrt{7}}{4}right) in simplest form?

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Accepted Answer

Step:1 ：Given the function f(x) = sin^{-1}(x), we need to find the derivative f&#x27;(x) and then evaluate it at x = frac{sqrt{7}}{4}.Step:2 ：Using the chain rule, we find the derivative of f(x): f&#x27;(x) = frac{1}{sqrt{1 - x^2}}.Step:3 ：Substitute x = frac{sqrt{7}}{4} into the derivative: f&#x27;left(frac{sqrt{7}}{4}right) = frac{1}{sqrt{1 - left(frac{sqrt{7}}{4}right)^2}}.Step:4 ：Simplify the expression: f&#x27;left(frac{sqrt{7}}{4}right) = frac{4}{3}.Step:5 ：(boxed{frac{4}{3}}) is the value of f&#x27;left(frac{sqrt{7}}{4}right) in simplest form.

Answer

Step: 1 ：Given the function f(x) = sin^{-1}(x), we need to find the derivative f&#x27;(x) and then evaluate it at x = frac{sqrt{7}}{4}.Step: 2 ：Using the chain rule, we find the derivative of f(x): f&#x27;(x) = frac{1}{sqrt{1 - x^2}}.Step: 3 ：Substitute x = frac{sqrt{7}}{4} into the derivative: f&#x27;left(frac{sqrt{7}}{4}right) = frac{1}{sqrt{1 - left(frac{sqrt{7}}{4}right)^2}}.Step: 4 ：Simplify the expression: f&#x27;left(frac{sqrt{7}}{4}right) = frac{4}{3}.Step: 5 ：(boxed{frac{4}{3}}) is the value of f&#x27;left(frac{sqrt{7}}{4}right) in simplest form.

If $f (x) = \sin^{- 1} (x)$ , then what is the value of $f^{'} (\frac{\sqrt{7}}{4})$ in simplest form?

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If f(x)=sin−1⁡(x), then what is the value of f′(74) in simplest form?

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If $f (x) = \sin^{- 1} (x)$ , then what is the value of $f^{'} (\frac{\sqrt{7}}{4})$ in simplest form?