sec x tan x
d/dx sec x
The trigonometric expression sec x tan x can be simplified using the trigonometric identity for tangent and secant:
tan x = sin x / cos x
sec x = 1 / cos x
Substituting the expressions for tangent and secant, we get:
sec x tan x = (1 / cos x) * (sin x / cos x)
Multiplying the numerator and denominator, we get:
sec x tan x = sin x / (cos x)^2
Therefore, the simplified form of sec x tan x is sin x / (cos x)^2.
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