Question

what is the deravative of sec x​

Answer 1

Step-by-step explanation:

Let us assume that sec x= 1/cos x

Now will use the quotient rule

{The quotient rule of differentiation is defined as the ratio of two functions (1st function / 2nd Function), is equal to the ratio of (Differentiation of 1st function × the 2nd function – Differentiation of second function × the 1st function) to the square of the 2nd function.

f′(x)=[s(x) / t(x)]′=t(x).s′(x)–s(x).t′(x) / {t(x)}2 }

So by the above mentioned quotient rule

quotient rule derivative of secx = 1/cosx

= ddx×1–ddxcosx×1(cosx)2

On simplifying the equation we get

= 0×cosx–ddxcosx×1(cosx)2

= sinx(cosx×cosx)

= (sinxcosx)(1cosx)

=tanx. secx

Answer

Derivative of sec x = tanx. secx

Answer 2

Answer:

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