I'm still trying to solve this derivative :(

In summary, the conversation was about a user submitting a Word document with incorrect calculations for finding the derivative of a function with two variables. The person helping them pointed out the errors and suggested using parentheses for clarity. The user was also advised to avoid posting Word attachments and to continue with the previous thread for assistance.
  • #1
Maniac_XOX
86
5
Homework Statement
I've submitted a similar thread previously but messed it all up so here's a second try. The objective is to find the first and second partial derivative of the function z = tan x^2*y^2
Relevant Equations
tan x^2*y^2 = (sin x^2*y^2)/(cos x^2*y^2)
quotient rule: if z= f/g, z' = (f'*g - f*g')/g^2
I have attached a word document demonstrating the working out cos i was too lazy to learn how Latex primer works and writing it like I did above would've been too hard too read. I tried to make it as understandable as possible, presenting fractions as
' a ' instead of ' a / b ' .
------
b
 

Attachments

  • Find the first and second derivative of z.docx
    12.5 KB · Views: 225
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  • #2
I was able to open the Word document, but your work starts off with an error.
From the Word doc:
Since I started with finding the derivative in respect to x, throughout the calculation I treated y^2 as constant 'a'
No, that's not correct. Your function is ##z = \tan(x^2y^2)##, so z is a function of both x and y. Unless both x and y are themselves functions of some other variable (such as t, for example), there is no derivative dz/dx.

In this case there are two first (partial) derivatives: ##\frac{\partial z}{\partial x}## and ##\frac{\partial z}{\partial y}##. And there are four second partials ##\frac{\partial^2 z}{\partial x^2}##, ##\frac{\partial^2 z}{\partial y^2}##, and the two mixed partials. You were told all of this in the other thread you started.

The two first partials aren't too hard if you leave ##\tan(x^2y^2)## as it is and don't write it as a quotient. You do know the formula for the derivative of tan(x), don't you? It greatly complicates matters to take the derivative of sin(x)/cos(x).

One more thing. Please use parentheses around the arguments to any trig function. I realize that textbooks often write things like ##\sin \theta##, but as soon as the function arguments get more complicated, it really helps to add in the parentheses. tan x^2*y^2 is ambiguous, but tan(x^2*y^2) is perfectly clear.
 
  • #3
Ray Vickson said:
Is your function ##\tan(x^2) + y^2 = y^2 + \tan x^2?## That is what you wrote. If you mean ##\tan(x^2+y^2)## you need to write parentheses, to keep the things sorted out properly.

You do not need to use LaTeX (although it will be worth your effort in the long run); you can just use plain typwriter text, like this: tan(x^2 +y^2). That is perfectly clear to everybody. You can even write things like (d/dx) tan(x^2+y^2), to indicate a partial derivative wrt x.

I was not able to get the word file to open properly on my laptop, and not open at all on my i-phone. You should avoid posting word attachments if you are really serious about wanting help
No the * sign stands for multiplication so it's ##\tan (x^2 * y^2)##
 
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Likes Questionable Thought

1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is the slope of the tangent line to the function at that point.

2. Why is solving derivatives important?

Solving derivatives is important because it allows us to find the maximum and minimum values of a function, determine the rate of change of a function, and solve optimization problems in various fields such as physics, economics, and engineering.

3. What are the basic rules for solving derivatives?

The basic rules for solving derivatives include the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of a wide range of functions.

4. How do I know if I have solved a derivative correctly?

To check if you have solved a derivative correctly, you can use the first and second derivative tests to analyze the behavior of the function. Additionally, you can use online derivative calculators or check your work with a peer or teacher.

5. What are some common mistakes to avoid when solving derivatives?

Some common mistakes to avoid when solving derivatives include not applying the correct rules, making algebraic errors, and forgetting to simplify the final answer. It is important to double-check your work and practice regularly to avoid these mistakes.

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