deriv of secx
secxtanx
To find the derivative of sec x, we start with the fundamental formula of trigonometry:
sec²x = 1 + tan²x
Taking the derivative of both sides of the equation with respect to x, we get:
2sec x * sec x’ = 2tan x * sec²x * tan’x
Simplifying, we get:
sec x * sec x’ = tan x * sec²x * tan’x
Dividing both sides by sec x, we get the derivative of sec x:
sec x’ = tan x * sec x * tan’x
Therefore, the derivative of sec x is equal to the product of tan x and sec x, multiplied by the derivative of tan x. We can also express the derivative of sec x in terms of sine and cosine:
sec x’ = sec x * tan x * tan’x = sec x * sin x / cos x = sin x / (cos x)²
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