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If x = sin y what is the rate at which y changes with respect to x.

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f32 | Student, Grade 9 | (Level 1) Honors

Posted July 2, 2013 at 2:06 PM via web

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If x = sin y what is the rate at which y changes with respect to x.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 2, 2013 at 2:10 PM (Answer #1)

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The function x = sin y. The rate of change of y with respect to x is `dy/dx` .

x = sin y

Take the derivative of both the sides with respect to x.

=> `1 = cos y*(dy/dx)`

=> `dy/dx = 1/cos y`

=> `dy/dx = 1/sqrt(1- sin^2y)`

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

The rate of change of y with respect to x is `1/sqrt(1- x^2)`

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