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Find dy/dx if y=cos^−1(√x) - Mathematics and Statistics

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Sum

Find `dy/dx if y=cos^-1(sqrt(x))`

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Solution

`"Let" y=cos^(-1)sqrtx`

Differentiating w.r.t x

`dy/dx=d/dx(cos^(-1)sqrtx)`

`=-1/(sqrt(1-(sqrtx)^2))d/dx(sqrtx)`

`=-1/sqrt(1-x)xx1/(2sqrtx)`

`dy/dx = (-1)/(2sqrt(x-x^2))`

Concept: The Concept of Derivative - Derivative of Inverse Function
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