How to Find the Derivative of tan(x) Using the Chain Rule

d/dx tan(x)

To find the derivative of the function f(x) = tan(x), we can use the chain rule

To find the derivative of the function f(x) = tan(x), we can use the chain rule. The chain rule states that if y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).

In this case, let’s consider f(x) = tan(x). The derivative of tangent with respect to x is given by:

d/dx tan(x)

Applying the chain rule, we can let g(x) = x, so g'(x) = 1. And f'(x) represents the derivative of the tangent function, which is given by:

f'(x) = sec^2(x)

Now, substituting these values into the chain rule formula:

d/dx tan(x) = f'(g(x)) * g'(x)
= sec^2(x) * 1
= sec^2(x)

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

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