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Course: Calculus I
Topic: Derivatives
Subtopic: Product Rule, Quotient Rules, & Deriv. of Trig Functions

Overview

If we wish to take a derivative of, for example, x/sinx, we need a rule for taking the derivative of a quotient. Not surprisingly, there is one, and it is called the quotient rule. That along with the product rule, which finds the derivative of a produce such as xex, allow up to find the derivatives of the remaining four trigonometric functions.

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Terms you should be able to define: product rule, quotient rule

Product Rule

`d/dx(f(x)*g(x))=f(x)*g'(x)+f'(x)*g(x)`

Or as a mnemonic:
`(F*L)'=F*L'+F'*L`
where F = first function
and L = last function

Quotient Rule

`d/dx(f(x)/g(x))=(f(x)*g'(x)-f'(x)*g(x))/g^2(x)`

Or as a mnemonic:
`(N/D)'=(D*N'-N*D')/D^2`
where N = numerator, D = denominator


Derivatives of the Trigonometric Functions

`d/dx(sinx) = cosx`

`d/dx(tanx) = sec^2x`

`d/dx(secx) = secx tanx`

`d/dx(cosx) = -sinx`

`d/dx(cotx) = -csc^2x`

`d/dx(cscx) = -cscx cotx`

Text Notes

Mini-Lectures and Examples

STUDY: Derivatives - Product Rule, Quotient Rule, and Trig Functions

Supplemental Resources (optional)

Video: Derivatives of Trigonometric Functions, Selwyn Hollis's Video Calculus

Lesson: Differentiation Formulas, Dale Hoffman's Contemporary Calculus
and More Differentiation Formulas, Dale Hoffman's Contemporary Calculus.

rev. 2020-10-10