Mastering Derivatives: Step-By-Step Guide To Using Chain Rule In Differentiating Tan(X)

d/dx(tanx)

sec²x

We will use the chain rule to differentiate the given function.

Let y = tan(x)

Using the derivative of tan(x), we know that

y’ = sec^2(x)

Now, applying chain rule we get

(d/dx) tan(x) = (d/dx) y = (d/dx) sec^2(x) = sec^2(x) (d/dx) x = sec^2(x)

Therefore, the derivative of tan(x) is sec^2(x).

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