SOLUTION: if y=f((2x-1)/(x^2+1)) , f'(x)=sin(x^2) find dy/dx

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Question 1117134: if y=f((2x-1)/(x^2+1)) , f'(x)=sin(x^2) find dy/dx
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
y is a function of a function of x .
The function g%28x%29=%282x-1%29%2F%28x%5E2%2B1%29 operates on x ,
and then a mysterious f%28g%29 function, such that %22f+%27+%28+x+%29%22=sin%28x%5E2%29 operates on the result.
You calculate the derivative of a function like that using the “chain rule.”

dg%2Fdx%22=%22%282%28x%5E2%2B1%29-2x%282x-1%29%29%2F%28x%5E2%2B1%29%5E2%22=%22%282x%5E2%2B2-4x%5E2%2B2x%29%2F%28x%5E2%2B1%29%5E2%22=%22%28-2x%5E2%2B2x%2B2%29%2F%28x%5E2%2B1%29%5E2%22=%22-2%28x%5E2-x-1%29%2F%28x%5E2%2B1%29%5E2

It was hard to wrap my head around this problem,
but if I did not get myself hopeless confused,
dy%2Fdx%22=%22%22=%22%22f+%27+%22%28%282x-1%29%2F%28x%5E2%2B1%29%29%28-2%28x%5E2-x-1%29%2F%28x%5E2%2B1%29%5E2%29%22=%22%28sin%28%282x-1%29%5E2%2F%28x%5E2%2B1%29%5E2%29%29%28-2%28x%5E2-x-1%29%2F%28x%5E2%2B1%29%5E2%29%22=%22%28-2%28x%5E2-x-1%29%2F%28x%5E2%2B1%29%5E2%29sin%28%282x-1%29%5E2%2F%28x%5E2%2B1%29%5E2%29 .