# Derivatives of trigonometric functions

• MHB
• jhe2
In summary, the conversation discusses the derivative of the function y=5tanx+4cotx and the discrepancy between the answers provided by the website Math Help and the user's own calculation. The user realizes their mistake and acknowledges that the answer provided by Math Help is correct. They also ask for clarification on the source of the first answer.
jhe2
The answer for derivative of y=5tanx+4cotx is y'=-5cscx^2. But how come on math help the answer is 5sec^2x-4csc^2x? I have a calculus test coming up and I really would appreciate if someone could explain!

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Oh nvm I see my mistake!

Hello, and welcome to MHB! (Wave)

The second answer you cited agrees with what W|A outputs as the derivative for the given function. If the two answers are equivalent, then the following will be an identity (I am assuming you mean something a bit different from the first answer):

$$\displaystyle -5\csc^2(x)=5\sec^2(x)-4\csc^2(x)$$

$$\displaystyle -\csc^2(x)=5\sec^2(x)$$

This is not an identity, so the first result you posted isn't correct. Where did this first result come from?

## What are derivatives of trigonometric functions?

Derivatives of trigonometric functions are mathematical functions that represent the rate of change or slope of a trigonometric function at any given point. They are used to analyze the behavior of trigonometric functions and determine the instantaneous rate of change.

## What is the general formula for finding derivatives of trigonometric functions?

The general formula for finding derivatives of trigonometric functions is: d/dx [f(x)] = f'(x) = lim(h->0) [f(x+h) - f(x)]/h, where f(x) is the trigonometric function and f'(x) is its derivative.

## How are derivatives of trigonometric functions used in real-world applications?

Derivatives of trigonometric functions are used in many real-world applications, such as physics, engineering, and economics. For example, they can be used to calculate the velocity of a moving object, the rate of change of a stock market index, or the slope of a ramp for wheelchair accessibility.

## What are the basic derivative rules for trigonometric functions?

The basic derivative rules for trigonometric functions are: d/dx [sin(x)] = cos(x), d/dx [cos(x)] = -sin(x), d/dx [tan(x)] = sec^2(x), and d/dx [cot(x)] = -csc^2(x). These rules can be extended to other trigonometric functions using the quotient, product, and chain rules.

## How can I use derivatives of trigonometric functions to solve problems?

To solve problems using derivatives of trigonometric functions, you can follow the steps of differentiation to find the derivative of the given trigonometric function. Then, you can use the derivative to analyze the behavior of the function, find its maximum and minimum values, and solve related optimization problems.

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