Derivative of this trig function is: d/dx[sec(x/12)]=sec(x/12)*tan(x/12)*d/dx(x/12)=sec(x/12)*tan(x/12) If chain rule is not applied to this function like this because the function is "composite" which is why it should be done as the first variant, then how was chain rule altered for this function in the first variant?

Spactapsula2l

Spactapsula2l

Answered question

2022-09-12

Derivative of this trig function is:
d d x [ sec ( x 12 ) ]   = sec ( x 12 ) tan ( x 12 ) d d x ( x 12 ) = sec ( x 12 ) tan ( x 12 ) 1 12
If chain rule is not applied to this function like this because the function is "composite" which is why it should be done as the first variant, then how was chain rule altered for this function in the first variant?

Answer & Explanation

ko1la2h1qc

ko1la2h1qc

Beginner2022-09-13Added 18 answers

Actaully it is the chain rule. You are confusing the chain rule and the power rule. If h ( x ) = f ( g ( x ) ), the chain rule states:
h ( x ) = f ( g ( x ) ) g ( x )
The power rule is just a special case of the chain rule. Namely, when f ( x ) = x n .
To use the chain rule for your example. Let f ( x ) = sec x and g ( x ) = x 12 .
h ( x ) = f ( g ( x ) ) = f ( x 12 ) = sec x 12
So,
h ( x ) = f ( g ( x ) ) g ( x ) = sec x 12 tan x 12 1 12 = 1 12 sec x 12 tan x 12 .

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