Implicit DifferentiationFinding dy/dx for a curve where y is never isolated.MathematicsFor a curve given by an equation in x and y together.1Differentiate both sidesApply d/dx to every term, treating y as an unknown function of x.2Chain rule on every y termEach y term picks up a factor dy/dx, so d/dx(y³) = 3y² dy/dx.3Product rule on mixed termsd/dx(xy) = y + x dy/dx. Any term in both variables needs it.4Collect the dy/dx termsMove every term containing dy/dx to one side, the rest to theother.5Factor and divideFactor out dy/dx and divide. The answer usually involves x and yboth.Worked: x² + y² = 25 gives 2x + 2y dy/dx = 0, so dy/dx = −x/y —undefined at y = 0, where the tangent is vertical.Implicit Differentiationlearnposters.com
Implicit Differentiation — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

Implicit Differentiation, step by step

For a curve given by an equation in x and y together.

  1. Differentiate both sidesApply d/dx to every term, treating y as an unknown function of x.
  2. Chain rule on every y termEach y term picks up a factor dy/dx, so d/dx(y³) = 3y² dy/dx.
  3. Product rule on mixed termsd/dx(xy) = y + x dy/dx. Any term in both variables needs it.
  4. Collect the dy/dx termsMove every term containing dy/dx to one side, the rest to the other.
  5. Factor and divideFactor out dy/dx and divide. The answer usually involves x and y both.

Worked: x² + y² = 25 gives 2x + 2y dy/dx = 0, so dy/dx = −x/y — undefined at y = 0, where the tangent is vertical.

Questions about the Implicit Differentiation poster

What’s on the Implicit Differentiation poster?
5 numbered steps. For a curve given by an equation in x and y together. Differentiate both sides — Apply d/dx to every term, treating y as an unknown functio…; Chain rule on every y term — Each y term picks up a factor dy/dx, so d/dx(y³) = 3y² d…; Product rule on mixed terms — d/dx(xy) = y + x dy/dx. Any term in both variables need…; Collect the dy/dx terms — Move every term containing dy/dx to one side, the rest to t…; Factor and divide — Factor out dy/dx and divide. The answer usually involves x and y…. Worked: x² + y² = 25 gives 2x + 2y dy/dx = 0, so dy/dx = −x/y — undefined at y = 0, where the tangent is vertical.
Who is the Implicit Differentiation poster for?
Implicit Differentiation belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning calculus can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Implicit Differentiation poster?
For circles, conics and any relation F(x, y) = 0 that will not solve for y. A wall chart earns its place by being glanceable from where the work is happening, so Implicit Differentiation belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Implicit Differentiation?
The Chain Rule, Derivative Rules and Fundamental Theorem sit alongside Implicit Differentiation in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Chain RuleDerivative RulesFundamental Theorem
Is the Implicit Differentiation poster free to download and print?
Yes. Implicit Differentiation downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Implicit Differentiation poster print at?
Implicit Differentiation is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Implicit Differentiation loses nothing.Printing guide

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