## What is the dy dx of tan?

The derivative of tanx is sec2x .

**What is the derivative of tan to the?**

The derivative of tan x is sec2x. When the tangent argument is itself a function of x, then we use the chain rule to find the result.

**What is the first derivative of tangent?**

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!

### How to find the derivative of tan ( x )?

In the following practice problems, students will find the derivative of the tangent of a function of x using the chain rule. Students will also derive the formula for the derivative of cotangent using the same method used to find the derivative of tangent. 1. Find the derivative of f (x) = tan (9x – 2).

**How to find the 99th derivative of sin x?**

Hint. One may prove that d 99 d x 99 ( sin x) = sin ( x + 99 π 2) = sin ( x + 48 π + 3 π 2) = − cos x. again. That is because doing the 96’th derivative is the same as doing 4th derivative 24 times and doing the 4th derivative didn’t do anything. Now you just have to do 3 more to get 99 from 96.

**When to apply the quotient rule to tan x?**

The quotient rule says that if two functions are differentiable, then the quotient is also differentiable. Here’s the quotient rule applied to tan x when in form of sin x /cos x: Now we know that the derivative of sin x is cos x and the derivative of cos x is -sin x. Substituting these derivatives in the parentheses and simplifying, we get:

## How to prove the derivative of arctan ( x )?

Therefore, we may prove the derivative of arctan (x) by relating it as an inverse function of tangent. Here are the steps for deriving the arctan (x) derivative rule. 3.) Using sum of squares corollary: sec 2 (y) = 1 + tan 2 (y) 5.) Flipping dx/dy, we get dy/dx = 1/ (1 + x2)