d/dx secx
secxtanx
To find the derivative of sec x with respect to x, we can start by using the quotient rule.
Recall that for a function u(x) divided by v(x), the quotient rule states that the derivative is given by:
(u/v)’ = (u’v – uv’)/v^2
In this case, we can take u(x) = 1 and v(x) = cos x, since sec x = 1/cos x. Then, we have:
sec x = 1/cos x
u(x) = 1
v(x) = cos x
Using the quotient rule, we get:
d/dx(sec x) = d/dx(1/cos x)
= (-1(cos x)’ – 1′(cos x))/cos^2 x
= (-(-sin x))/cos^2 x
= sin x/cos^2 x
= sin x sec x
Therefore, the derivative of sec x with respect to x is sin x sec x.
More Answers:
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