## How do you take the derivative of a tangent?

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The formula for differentiation of tan x is,

- d/dx (tan x) = sec2x (or)
- (tan x)’ = sec2x.

**How do you find the tangent line using the Mean Value Theorem?**

The theorem is stated as follows. Figure 1 The Mean Value Theorem. Geometrically, this means that the slope of the tangent line will be equal to the slope of the secant line through (a,f(a)) and (b,f(b)) for at least one point on the curve between the two endpoints.

### What is tangent the derivative of?

The derivative of tangent is secant squared and the derivative of cotangent is negative cosecant squared.

**Is the tangent line the derivative?**

The derivative is not the same thing as a tangent line. Instead, the derivative is a tool for measuring the slope of the tangent line at any particular point, just like a clock measures times throughout the day. With this in mind, you’ll have no trouble tackling tangent line problems on the AP Calculus exam!

#### Is Rolle’s theorem the same as MVT?

Rolle’s theorem is clearly a particular case of the MVT in which f satisfies an additional condition, f(a) = f(b).) The applet below illustrates the two theorems. It displays the graph of a function, two points on the graph that define a secant and a third point in-between to which a tangent to the graph is attached.

**Is the first derivative the tangent line?**

The first derivative of a function is the slope of the tangent line for any point on the function! Therefore, it tells when the function is increasing, decreasing or where it has a horizontal tangent!

## Why is the derivative the slope of the tangent?

The Derivative Measures Slope By plugging in different input values, x = a, the output values of f ‘(x) give you the slopes of the tangent lines at each point x = a. This is what we mean when we say that “the derivative measures the slope of the tangent lines.”