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).


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).


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:


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Applying the Rules of Differentiation to Calculate Derivatives


Chapter 8 / Lesson 13

The rules of differentiation are useful to find solutions to standard differential equations. Identify the application of product rule, quotient rule, and chain rule to solving these equations through examples.

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