009A Sample Final 1, Problem 4

If

$y=x^{2}+\cos(\pi (x^{2}+1))$

compute ${\frac {dy}{dx}}$ and find the equation for the tangent line at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_0=1} . You may leave your answers in point-slope form.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Step 3:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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