Understanding the Derivative of f(x) = Tan(x) Using the Chain Rule

d/dx(tanx)

To find the derivative of the function f(x) = tan(x), we can use the basic differentiation rules

To find the derivative of the function f(x) = tan(x), we can use the basic differentiation rules. The derivative of tan(x) can be found by applying the chain rule.

The chain rule states that if we have a composite function, such as f(g(x)), then the derivative of the composite function with respect to x is given by:

(d/dx) f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to the function f(x) = tan(x), we can let g(x) = x, and f(g(x)) = f(x) = tan(x).

So, we have:

(d/dx) f(x) = f'(x) * g'(x)

Now, let’s find the derivatives of f(x) = tan(x) and g(x) = x:

First, let’s find the derivative of g(x) = x, which is simply 1.

So, g'(x) = 1.

Now, let’s find the derivative of f(x) = tan(x). We can write it as f(u), where u = x, and apply the chain rule:

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

Since u = x, we have f'(x) = sec^2(x).

Now, we can substitute these values into the chain rule formula:

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

Therefore, the derivative of f(x) = tan(x) is d/dx(tan(x)) = sec^2(x).

More Answers: