3.5 Derivatives Of Trig Functions
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Transcript of 3.5 Derivatives Of Trig Functions
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Derivatives of Trigonometric
Functions
Derivatives of Trigonometric
Functions
![Page 2: 3.5 Derivatives Of Trig Functions](https://reader036.fdocuments.in/reader036/viewer/2022082605/5562d7d2d8b42a63498b50ba/html5/thumbnails/2.jpg)
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
![Page 3: 3.5 Derivatives Of Trig Functions](https://reader036.fdocuments.in/reader036/viewer/2022082605/5562d7d2d8b42a63498b50ba/html5/thumbnails/3.jpg)
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
![Page 4: 3.5 Derivatives Of Trig Functions](https://reader036.fdocuments.in/reader036/viewer/2022082605/5562d7d2d8b42a63498b50ba/html5/thumbnails/4.jpg)
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
![Page 5: 3.5 Derivatives Of Trig Functions](https://reader036.fdocuments.in/reader036/viewer/2022082605/5562d7d2d8b42a63498b50ba/html5/thumbnails/5.jpg)
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.
![Page 6: 3.5 Derivatives Of Trig Functions](https://reader036.fdocuments.in/reader036/viewer/2022082605/5562d7d2d8b42a63498b50ba/html5/thumbnails/6.jpg)
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
![Page 7: 3.5 Derivatives Of Trig Functions](https://reader036.fdocuments.in/reader036/viewer/2022082605/5562d7d2d8b42a63498b50ba/html5/thumbnails/7.jpg)
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
![Page 8: 3.5 Derivatives Of Trig Functions](https://reader036.fdocuments.in/reader036/viewer/2022082605/5562d7d2d8b42a63498b50ba/html5/thumbnails/8.jpg)
Do page 146 (1 - 10) for HW
Do page 146 (1 - 10) for HW