Differentiation of Trigonometric functions

In summary, the derivative of y = tan2(3x-2) is 6*tan(3x-2)*sec2(3x-2). This can be confirmed by using the power rule and the chain rule. Happy new year!
  • #1
MaxManus
277
1

Homework Statement


Let y = tan2(3x-2)
Find dy/dx


The solution is:
2*tan(3x-2)*sec(3x-2)*3
= 6*tan(3x-2)*sec2(3x-2)

Why is it not:
6*tan(3x-2)*sec(3x-2)

I am thinking:
y = (tan(3x-2))2
take the power 2 down,multiply with the parentes multiply with the defferentiated parentes

Edit: Happy new year
 
Physics news on Phys.org
  • #2
happy new year!

MaxManus said:
Let y = tan2(3x-2)
Find dy/dx
…
Why is it not:
6*tan(3x-2)*sec(3x-2)

I am thinking:
y = (tan(3x-2))2
take the power 2 down,multiply with the parentes multiply with the defferentiated parentes

Hi MaxManus! Happy new year! :smile:

(what are parentes? :confused: do you mean "parenthesis"?)

y = (thing)2,

so y' = 2(thing)(thing') …

in this case, the thing is a tan, and tan' = sec2 :wink:
 
  • #3
What do you think d(tan(u))/dx is equivalent to?

Edit: tiny-tim beat me to it.
 
  • #4
happy new year!

jgens said:
Edit: tiny-tim beat me to it.

na na na na-na! :-p

hic! :redface:

:smile: happy new year! :smile:​
 
  • #5
Happy new year! :)
 
  • #6
Thanks tiny-tim and jgens.
Yes, I ment parenthesis, but I could not spell it.
 
  • #7
Hitting the champagne a little early?
 

FAQ: Differentiation of Trigonometric functions

1. What is the definition of differentiation of trigonometric functions?

The differentiation of trigonometric functions is the process of finding the rate of change of a trigonometric function with respect to its independent variable. It involves finding the derivative of the function, which represents the slope of the function at a given point.

2. What are the basic rules for differentiating trigonometric functions?

The basic rules for differentiating trigonometric functions include using the power rule, product rule, quotient rule, and chain rule. These rules can be applied to individual trigonometric functions or to combinations of trigonometric functions.

3. How do you differentiate sine and cosine functions?

To differentiate a sine or cosine function, you can use the power rule and chain rule. For example, the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x).

4. Can trigonometric identities be used in differentiation?

Yes, trigonometric identities can be used to simplify the differentiation of trigonometric functions. For example, the double angle identities can be used to rewrite a function in a more manageable form before differentiating.

5. What are the applications of differentiation of trigonometric functions?

The differentiation of trigonometric functions is used in various fields such as physics, engineering, and economics. It can be used to model and analyze periodic phenomena, calculate rates of change, and optimize functions.

Similar threads

Question on Two Differentiation Techniques
Replies
25
Views
1K
What Function Satisfies the Derivative Equation in Complex Analysis?
Replies
1
Views
945
[Calc] First max and min values of an underdamped oscillation
Replies
10
Views
2K
Solve the given first order differential equation
Replies
8
Views
1K
Calculate this Integral around the Circular Path using Green's Theorem
Replies
3
Views
1K
Solve this problem that involves implicit differentiation
Replies
15
Views
1K
Calculus ## G(y, z)=z\frac{\partial}{\partial z}F(y, z)-F(y, z) ##?
Replies
6
Views
1K
How do I differentiate the function F(x)=4^{3x}+e^{2x}?
Replies
5
Views
1K
Differentiating Trigonometric Functions: Find the Derivatives
Replies
10
Views
2K
Computing the polar moment of inertia (calculus)
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top