Q:
# What Is the Derivative of Tan 2x?

**The derivative of tan(2x) is equal to two times the secant squared of two times x.** Using mathematical notation, the equation is written as d/dx tan(2x) = 2sec^2(2x).

The derivative of tan(2x) can be found by using the quotient rule and the chain rule. Using the quotient rule, the tangent of 2x can be simplified to read the cosine squared of 2x plus the sine squared of 2x divided by the cosine squared of 2x. Using the Pythagorean identity, this equation further simplifies to one over the cosine squared of 2x. The inverse of cosine squared 2x is the secant squared of 2x. With the chain rule, the derivative of 2x is two.

Learn more about Calculus-
Q:
## What Is the Derivative of Y = Arctan(6x)?

A: The derivative of y = arctan(6x) is 6/(1 + 36 x^2). To arrive at this answer, it is simply a matter of using the formula given for finding the derivative o... Full Answer >Filed Under: -
Q:
## What Is the Derivative of Sin Squared?

A: The derivative of sine squared is the sine of 2x, expressed as d/dx (sin2(x)) = sin(2x). The derivative function describes the slope of a line at a given p... Full Answer >Filed Under: -
Q:
## What Is Instantaneous Velocity in Calculus?

A: The instantaneous velocity in calculus is the first derivative of a function that expresses distance as a function of time. The instantaneous velocity is a... Full Answer >Filed Under: -
Q:
## What Is the Derivative of the Square Root of X?

A: The derivative of the square root of x is one-half times one divided by the square root of x. The square root of x is equal to x to the power of one-half. Full Answer >Filed Under: