Derivada De La Funcion Trigonometrica

Introduction

We begin the work with definition of derivative, which is the mathematical process of finding the pace to which a trigonometrical function changes respect of theindependent variable; it is to say, the derivative of the function. The most habitual trigonometrical functions are the functions without (x), cos (x) and so (x). For example, on havingderived f (x) = sin (x), it is calculated the function f ' (x) such that gives the pace of change of the sin (x) in every point x

(1)F(x): 4x5 Cos59x2
A: 4x5A’: 20x4
B: Cos59x2 B’: 9.5Cos49x2. (-Sen9.9x2)
F(x): A’B + AB’
F(x): 20x4(Cos59x2) + 4x5 (9.5Cos49x2. (-Sen9.9x2))
F(x): 20x4 Cos49x2(Cos9x2 + 45x5 – Sen99x)
= 20x4 Cos49x2(Cos9x2 + 45x4(Cos9x + 1))
=20x4 Cos49x2(Cos9x2 + 45x49x2 + 9x2)


(2)F(x): Tan57x5 % 2x5
A: Tan57x5 B: 2x5
A’:5.Tan47x.7.Sec2 7x B’:10x4
B2: 25Tan4 7x.Sec 7x

F(x): (5Tan3 7x5) (Tan7x5)(Sec4x5) 25x4
25Tan4 7x.Sec 7x

F(x): 125x4 Tan57x5 . Sec4x5 __= 125Cos . 25Csc47x
25Sec47x 25Sec47x

(3)F(x): Cos 57x5
Sen57x

A: Cos 57x5 A’: -5Sen57x5

B: Sen57xB’: 7.5 Sen7x.(Cos7. 7x)
B2: 35 Cos7x
F(x): A’B – AB’
B2

F(x) : -5Sen57x5(Sen57x) - Cos 57x5 (7.5 Sen7x.(Cos7. 7x))35 Cos7x

F(x): Sen7x(-5Sen57x5Sen7x – Cos 57x Sen7x.(Cos7. 7x)
35 Cos7x

F(x): (-5Sen57x5Sen7x – Cos 57x Sen7x.(Cos7. 7x)35 Cos7x

(4)F(x): Tan77x5 % Cos57x3
F(x): 7. (5Tan6 7x.Sec 7x) (Sec77x3)(7x5) % 5.(Cos47x2.-Sen57x) (7x3)
F(x):175x2. Sec77x2. Sen57x2