Mastering the Quotient Rule: Deriving the Secant Squared of Tan(x)

tan(x)’ =

The derivative of tan(x) can be computed using the quotient rule

The derivative of tan(x) can be computed using the quotient rule.

Using the quotient rule, the derivative of tan(x) = d/dx(sin(x)/cos(x)):

= (cos(x) * d/dx(sin(x)) – sin(x) * d/dx(cos(x))) / (cos(x))^2

= (cos(x) * cos(x) – sin(x) * (-sin(x))) / (cos(x))^2

= (cos^2(x) + sin^2(x)) / (cos(x))^2

= 1 / (cos(x))^2

= sec^2(x)

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

More Answers:

How to Find the Derivative of the Function f(x) = arctan(x) Using the Definition of the Derivative
Proving the Derivative of sin(x) is cos(x) using the Limit Definition of Derivative
Understanding the Chain Rule: Finding the Derivative of cosine(x)

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