User: You are given access to make searches on the Internet. The format for making a search is: 1. The user sends a message. 2. You will decide whether to make a search. If you choose to make a search, you will output a single message, containing the word 
 (EXACTLY AS IT IS GIVEN TO YOU), followed by ONLY your web search query. After outputting your search query, you MUST output the token 
 (EXACTLY AS IT IS GIVEN TO YOU) to denote the end of the search query. Keep your search query concise as there is a 400 characters limit.
The system will then append the web search results at the end of the user message, starting with the token 
. Take note that the user CANNOT ACCESS the content under 
 - YOU should incorporate these results into your response. Additionally, If the token 
 is present in the user's message, then you MUST NOT request another web search.

IMPORTANT! You should choose to search the web ONLY if ANY of the following circumstances are met:
1. User is asking about current events or something that requires real-time information (news, sports scores, 'latest' information, etc.)
2. User is asking about some term you are unfamiliar with (e.g. if it's a little-known term, if it's a person you don't know well, etc.)
3. User is asking about anything that involves numerical facts (e.g. distances between places, population count, sizes, date and time, etc.)
4. User explicitly asks you to search or provide links to references.
If the user's query does NOT require a web search, YOU MUST NEVER run one for no reason.
However, NEVER refuse to search the web if the user asks you to provide such information.

When using web search results, you are encouraged to cite references where appropriate, using inline links in standard markdown format.
You are also allowed to make use of web search results from previous messages, if they are STRONGLY RELEVANT to the current message.

When you are not running a web search, respond completely as per normal - there is NO NEED to mention that you're not searching. 
Do your best to be informative. However, you MUST NOT make up any information. If you think you might not know something, search for it.

Assistant: Understood. I will strictly follow these instructions in this conversation.
User: d/dx tanx


 for "d/dx tanx":

1.
URL: https://www.cuemath.com/calculus/derivative-of-tan-x/
Title: Derivative of Tan x - Formula, Proof, Examples - Cuemath
Content: Learn how to differentiate <b>tan</b> <b>x</b> using first principle, chain rule, and quotient rule. Find the formula, proof, and examples of <b>d/dx</b> (<b>tan</b> <b>x)</b> = sec 2 x.

2.
URL: https://www.symbolab.com/solver/step-by-step/%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft(tanx%5Cright)
Title: derivative of tanx - Symbolab
Content: \frac{d}{dx}\left(tanx\right) en. Related Symbolab blog posts. Practice, practice, practice. Math can be an intimidating subject. Each new topic we learn has symbols and problems we have never seen. The unknowing... Enter a problem. Cooking Calculators.

3.
URL: https://www.mathway.com/popular-problems/Calculus/503911
Title: Find dy/dx y=tan(x) | Mathway
Content: Calculus. Find dy/dx y=tan (x) y = <b>tan</b> <b>(x)</b> y = <b>tan</b> <b>(x)</b> Differentiate both sides of the equation. <b>d</b> <b>dx</b> (y) = <b>d</b> <b>dx</b> (<b>tan</b>(x)) d d x (y) = d d x (<b>tan</b> <b>(x))</b> The derivative of y y with respect to x x is y' y ′. y' y ′. The derivative of <b>tan</b>(x) <b>tan</b> <b>(x)</b> with respect to x x is sec2(x) sec 2 (x). sec2(x) sec 2 (x)

4.
URL: https://www.wolframalpha.com/input/?i=d%2Fdx+tanx
Title: d/dx tanx - Wolfram|Alpha
Content: <b>d/dx</b> <b>tanx</b>. Have a question about using Wolfram|Alpha? Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….

5.
URL: https://www.mathsisfun.com/calculus/derivatives-trig-proof.html
Title: Derivatives of the Trigonometric Functions - Math is Fun
Content: Learn how to prove the derivatives of trigonometric functions using first principles and identities. Find out why <b>d/dx</b> <b>tanx</b> = sec2x and how to use the quotient rule.

6.
URL: https://calculator-derivative.com/derivative-of-tan
Title: Derivative of tan: Formula, Proof, Examples, Solution
Content: <b>d/dx</b>(tan <b>x)</b> = 1/cos 2 x = sec 2 x. Hence the <b>tan</b> <b>x</b> derivative is always equal to the square of secant x. Use product rule differentiation calculator for learning and practice online. How to find the derivative <b>tan</b> <b>x</b> with a calculator? The most easy way to differentiate <b>tanx</b> is by using an online tool. You can use our derivative calculator for this.

7.
URL: https://www.mathstoon.com/derivative-of-tan-x/
Title: Derivative of tan x: Proof by First Principle, Product ... - Mathstoon
Content: Learn how to find the derivative of <b>tan</b> <b>x</b> using limit, product, quotient and chain rules. See the formula, proof and solved problems on derivative of <b>tan</b> <b>x</b> and related functions.

8.
URL: https://scientificcalculatorsonline.com/derivative-of-tan-x/
Title: Derivative of Tan x: Formula, Rules &amp; Examples
Content: Learn how to find the derivative of <b>tan</b> <b>x</b> using the formula dy/dx = sec^2x and the chain rule. See examples of applying the formula and the rule to different functions involving <b>tan</b> <b>x.</b>

9.
URL: https://www.mathway.com/popular-problems/Calculus/501764
Title: Find the Derivative - d/dx xtan(x) | Mathway
Content: The derivative of <b>tan</b>(x) <b>tan</b> <b>(x)</b> with respect to x x is sec2(x) sec 2 (x). xsec2(x)+tan(x) <b>d</b> <b>dx</b> [x] x sec 2 (x) + <b>tan</b> <b>(x)</b> d d x [x] Differentiate using the Power Rule. Tap for more steps... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like ...

10.
URL: https://www.mathway.com/popular-problems/Calculus/508052
Title: Find the Derivative - d/dx tan(xy) | Mathway
Content: tan (xy) <b>tan</b> <b>(x</b> y) Differentiate using the chain rule, which states that <b>d</b> <b>dx</b> [f (g(x))] d d x [f (g (x))] is f '(g(x))g'(x) f ′ (g (x)) g ′ (x) where f (x) = <b>tan</b>(x) f (x) = <b>tan</b> <b>(x)</b> and g(x) = xy g (x) = x y. Tap for more steps... sec2(xy) d dx[xy] sec 2 (x y) d d x [x y] Differentiate. Tap for more steps... ysec2 (xy) y sec 2 (x y)

11.
URL: https://www.symbolab.com/solver/derivative-calculator
Title: Derivative Calculator - Symbolab
Content: The Derivative Calculator is an invaluable online tool designed to compute derivatives efficiently, aiding students, educators, and professionals alike. Here's how to utilize its capabilities: Begin by entering your mathematical function into the above input field, or scanning it with your camera. Click the 'Go' button to instantly generate the ...

12.
URL: https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.05%3A_Derivatives_of_Trigonometric_Functions
Title: 3.5: Derivatives of Trigonometric Functions - Mathematics LibreTexts
Content: Learn how to find the derivatives of the sine and cosine functions and their applications to simple harmonic motion. See proofs, graphs, and examples of the formulas for the derivatives of the sine and cosine functions.

13.
URL: https://en.neurochispas.com/calculus/derivative-of-tangent-tanx-formula-proof-and-graphs/
Title: Derivative of Tangent, tan(x) - Formula, Proof, and Graphs
Content: The Derivative of Tangent is one of the first transcendental functions introduced in Differential Calculus (or Calculus I). The derivative of the tangent function is equal to secant squared, sec2(x). We can prove this derivative using limits and trigonometric identities. In this article, we will discuss how to derive the trigonometric function ...

14.
URL: https://www.geeksforgeeks.org/derivative-of-tan-x/
Title: What is Derivative of Tan x? - Formula, Proof and Examples - GeeksforGeeks
Content: f'(x) = 2 tan x.d/dx(tan x) We know that the derivative of <b>tan</b> <b>x</b> is sec 2 x. f'(x) = 2 <b>tan</b> <b>x</b> · sec 2 x. Hence, derivative of the given function is 2 tan x·sec 2 x. Example 2: Differentiate <b>tan</b> <b>x</b> with respect to sec x. Solution: Let us assume v = <b>tan</b> <b>x</b> and u = sec x. Then dv/dx = sec2x and du/dx = sec x · <b>tan</b> <b>x.</b> We have to find dv/du. We can ...

15.
URL: https://www.epsilonify.com/mathematics/calculus/what-is-the-derivative-of-tanx/
Title: What is the Derivative of tan(x)? - [FULL SOLUTION] - Epsilonify
Content: We will find out what the derivative of \<b>tan</b>(x) is. We will be doing that by the fact that \<b>tan</b>(x) = \sin(x)/\cos(x) and apply the quotient rule. We saw earlier a difficult version how to show the derivative of \<b>tan</b>(x) with first principle method, but in this article, we take it more easier. Proof.


Assistant: