How to find (dy)/(dx) given sin y=x^2?

audioblogn8ci

audioblogn8ci

Answered question

2023-02-17

How to find d y d x given sin y = x 2 ?

Answer & Explanation

Zack Dawson

Zack Dawson

Beginner2023-02-18Added 8 answers

Differentiate the equation with respect to x :
sin y = x 2
y cos y = 2 x
y = 2 x cos y
If the function is only used for intervals, x [ 0 , 1 ] and y [ 0 , π 2 ] :
cos y = 1 - sin 2 y = 1 - x 4
so that:
y ( x ) = 2 x 1 - x 4

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