# a. {eq}y = \frac{\tan x \sec x}{1 - \cos x} {/eq}, find y'. b. {eq}f(t) = \sqrt{t^3 + 2 \cos t}, {/eq} find f'(0).

## Question:

a. {eq}y = \frac{\tan x \sec x}{1 - \cos x} {/eq}, find y'.

b. {eq}f(t) = \sqrt{t^3 + 2 \cos t}, {/eq} find f'(0).

## Derivatives:

In order to solve the given problem on derivatives, we will apply the basic rules and standard formulae of the differential calculus. In the first part, we will apply the "product rule" of the differential calculus. {eq}\begin{align*} \frac{d}{dx}(u \cdot v) = (u \cdot v' + v \cdot u') \end{align*} {/eq}.

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a. {eq}y = \frac{\tan x \sec x}{1 - \cos x} {/eq}. Find y'.

Differentiating the above by applying "product rule", we get:

{eq}\begin{al...