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Differentiate ='false' (a) f(x) = (sec x) x^2 ,(b) f(x) = In (sec x) + In (cot x)

Question:

Differentiate {eq}(a) f(x) = (sec x) x^2 ,(b) f(x) = In (sec x) + In (cot x) {/eq}

Differentiation:

For the first question, we will apply the product rule of differentiation. Th rule is:

(uv)'=uv'+vu'

For the second question, we will apply the chain rule of differentiation. The following differentiation formula are applicable to find the derivative of the given function:

{eq}\begin{align} \frac{d}{dx}\sec x&=\sec x\tan x \\ \frac{d}{dx}\cot x&=-\csc^2 x\\ \frac{d}{dx}\ln x=\frac{1}{x}\\ \frac{d}{dx}x^n&=nx^{n-1}\\ \end{align} {/eq}

Answer and Explanation:

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{eq}\begin{align} f(x)& = (\sec x) x^2\\ f'(x)& = (\sec x) \frac{d}{dx}x^2- x^2 \frac{d}{dx} (\sec x) \ \ \, (\text{ Apply the product rule of...

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Differentiation Strategy: Definition & Examples

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Chapter 7 / Lesson 15
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In this lesson, we'll learn about differentiation strategy. We'll define it and look at important characteristics. The lesson will then discuss the pros and cons of differentiation strategy.


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