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