Limits and functions

Calculus Level 3

Given,

\[\large y=\frac{1}{x^{2}+1}\]

Find \(y^{\prime}\) using the definition of the derivative.

\(x=\tan \alpha \) and \(y=\cos^2\alpha\) so that \(\dfrac{dy}{dx}=\dfrac{\frac{dy}{d\alpha}}{\frac{dx}{d\alpha}}\).

If \(y^{\prime}\) can be expressed as \(\large\frac {\alpha x }{ x^{ \beta }+2x^{ \gamma }+\delta } \).

What is the value of \( \alpha+\beta+\gamma+\delta\)?

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