# 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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