# 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}

Become a Study.com member to unlock this answer! Create your account

{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... Differentiation Strategy: Definition & Examples

from

Chapter 7 / Lesson 15
92K

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.