Derivatives of Trigonometric

Functions

Derivatives of Trigonometric

Functions

If y = sin x, then y’ = cos x

For example: If given y = 3x - 5 sinx

and asked to find y’

y’ = 3 - 5 cos x

If y = sin x, then y’ = cos x

For example: If given y = 3x - 5 sinx

and asked to find y’

y’ = 3 - 5 cos x

If y = cos x, then y’ = -sin x

For example:If given y = 7x2 + 2cos x

and asked to find y’you would get

y’ = 14x - 2sinx

If y = cos x, then y’ = -sin x

For example:If given y = 7x2 + 2cos x

and asked to find y’you would get

y’ = 14x - 2sinx

So you already know the derivatives of sin x and cos x. Here are the rest:

y y’sin x cos xcos x -sin xtan x sec2xcot x -csc2xsec x sec x tan xcsc x -csc x cot x

So you already know the derivatives of sin x and cos x. Here are the rest:

y y’sin x cos xcos x -sin xtan x sec2xcot x -csc2xsec x sec x tan xcsc x -csc x cot x

HINTS:All the derivatives of the “co”-functions are negatives.

They are also the opposite of whatever they are the co-function of.

For example:The derivative of tan x is sec2x, so the derivative of the co-function of tan x, cot x, is negative and the opposite of sec x, so you get -csc2x.

HINTS:All the derivatives of the “co”-functions are negatives.

They are also the opposite of whatever they are the co-function of.

For example:The derivative of tan x is sec2x, so the derivative of the co-function of tan x, cot x, is negative and the opposite of sec x, so you get -csc2x.

Examples:

y = 3 csc xy’ = -3 csc x cot x

y = 5x3 + tan xy’ = 15x2 + sec2x

Examples:

y = 3 csc xy’ = -3 csc x cot x

y = 5x3 + tan xy’ = 15x2 + sec2x

Product Rule and Quotient Rule still apply.

y = x2 sin x

y’ = uv’ + vu’

y’ = x2 cos x + sin x · 2xory’ = x2 cos x + 2x sin x

Product Rule and Quotient Rule still apply.

y = x2 sin x

y’ = uv’ + vu’

y’ = x2 cos x + sin x · 2xory’ = x2 cos x + 2x sin x

Do page 146 (1 - 10) for HW

Do page 146 (1 - 10) for HW