d/dx [tanx]
sec^2(x)
We can use the chain rule to find the derivative of tan(x).
Recall that the derivative formula of tan(x) is:
(d/dx) tan(x) = sec^2(x)
Using the chain rule, we obtain:
(d/dx) tan(x) = (d/dx) sec(u) * (du/dx) where u = x.
Let’s evaluate each term separately:
(d/dx) sec(u) = sec(u) * tan(u) by the derivative of sec(u) formula
(du/dx) = 1 since u = x and the derivative of x is 1.
Substituting values into the chain rule formula we get:
(d/dx) tan(x) = sec^2(x) * 1
= sec^2(x)
Therefore, the derivative of tan(x) is sec^2(x).
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