Master The Chain Rule: How To Easily Find The Derivative Of Tan(X)

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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