d/dx [ tan(x) ]
sec²(x)
To take the derivative of tan(x), we need to use the chain rule. The chain rule states that the derivative of a composition of functions is the product of the derivative of the outer function and the derivative of the inner function.
Let’s start by breaking down tan(x) as a composition of functions. We can write it as f(g(x)) where f(x) = tan(x) and g(x) = x.
f'(x) = sec^2(x) is the derivative of the outer function f(x) = tan(x).
g'(x) = 1 is the derivative of the inner function g(x) = x.
Using the chain rule, we get:
d/dx [tan(x)] = f'(g(x)) * g'(x) = sec^2(x) * 1 = sec^2(x)
Therefore, the derivative of tan(x) is sec^2(x).
More Answers:
Tanx: Definition, Formula, And PeriodicitySinx Function: Properties, Evaluation Techniques, And Applications In Mathematics And Physics
Mastering The Chain Rule: Differentiating Trigonometric Functions With A Math Specialist
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded