Derivative Trig

Derivative trig is used in finding derivative of trigonometric functions. The derivative of trig functions can be found by using definition of derivative and by using limit rules. It is a process of finding rate of change of trigonometric function with respect to a variable. Trigonometry is useful in areas such as astronomy, surviving, physics etc. Remember derivatives of basic 6 trigonometric functions. One derivative is shown in example 1.

Problem 1: Find the derivative of d (sin x) / dx

Solution: Given: d (sin x) / dx.

=> By the definition of derivative, d f(x) / dx = lim _h->0 f(x + h) – f(x) / h

=> d (sin x) / dx = lim _h->0 (sin (x+ h) – sin x) / h

= lim _h->0 (sin x cos h + sin h cos x – sin x) / h   (using trigonometric identity)

= lim _h->0 (sin x (cos h – 1) + sin h cos x) / h

= sin x lim _h->0 (cos h – 1) / h + cos x lim _h->0 (sin h) / h   (By separating the limits

=> By applying trigonometric limits we get, d (sin x) / dx = sin x. 0 + cos x. 1 = cos x

Problem 2: Find the derivative of d (2sec(x) – 5 cot (x))/dx

Solution: Given: d (2sec(x) – 5 cot(x))/dx

=> We know the derivative of basic 6 trigonometric functions

=> So, d sec (x) / dx = sec(x) tan(x) and also d cot(x)/dx = - csc^2(x)

=> d (2sec(x) – 5 cot(x))/dx = 2 sec(x) tan(x) – 5(- csc^2(x))

= 2 sec(x) tan(x) + 5 csc^2(x)

=> Therefore, the derivative of d (2sec(x) – 5 cot (x))/dx = 2 sec(x) tan(x) + 5 csc^2(x)


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