Trying to find dy/dx of a trig function

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SUMMARY

The discussion focuses on finding the derivative dy/dx for the equation x = tan(y). Participants emphasize that differentiation should be applied to both sides of the equation, leading to the correct application of the chain rule. The correct differentiation process involves using the formula d/dx(f(u)) = f'(u) * du/dx, which is essential for solving this type of problem. Missteps in applying the chain rule and misunderstanding the differentiation of equations are highlighted as common errors.

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  • Understanding of basic calculus concepts, specifically differentiation.
  • Familiarity with the chain rule in calculus.
  • Knowledge of trigonometric functions, particularly the tangent function.
  • Ability to manipulate and differentiate implicit equations.
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  • Study the application of the chain rule in calculus.
  • Practice differentiating implicit functions with examples.
  • Explore the properties and derivatives of trigonometric functions.
  • Learn about common mistakes in differentiation and how to avoid them.
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Students studying calculus, particularly those tackling implicit differentiation and trigonometric derivatives, as well as educators looking for clarification on common student errors in differentiation.

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Homework Statement


find dy/dx


Homework Equations


x= tan y


The Attempt at a Solution


d/dx(x=tanY)

1=(tan(dy/dx))+sec^2+y
 
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jtt said:

Homework Statement


find dy/dx


Homework Equations


x= tan y


The Attempt at a Solution


d/dx(x=tanY)
First off, you don't take the derivative of an equation - you take the derivative of each side of an equation.

The above should be d/dx(x) = d/dx(tan(y))

To carry out the differentiation on the right, you need to use the chain rule.

d/dx(f(u)) = d/du(f(u)) * du/dx = f'(u) * du/dx
jtt said:
1=(tan(dy/dx))+sec^2+y
Nope.
 

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