The Chain RuleDifferentiating a composition, and the factor everyone drops.MathematicsThe derivative of a composition is the outerderivative at the inner function, times the innerderivative.d/dx f(g(x)) = f′(g(x)) · g′(x)d/dx sin(3x²)6x cos(3x²)Outer sin, inner 3x².d/dx e^(−x²)−2x e^(−x²)Inner derivative −2x.d/dx (ln x)⁵5(ln x)⁴ / xPower outer, ln inner.THE COMMON MISTAKEd/dx sin(3x) = cos(3x)d/dx sin(3x) = 3 cos(3x)Forgetting the inner derivative is the commonest calculus slip. Differentiate theouter function, then multiply by the derivative of the inside.In Leibniz form dy/dx = (dy/du)(du/dx). The u must be a genuinefunction of x for that cancellation to mean anything.The Chain Rulelearnposters.com
The Chain Rule — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the The Chain Rule poster

The rule, 3 worked examples, and the mistake everyone makes.

In Leibniz form dy/dx = (dy/du)(du/dx). The u must be a genuine function of x for that cancellation to mean anything.

Questions about the The Chain Rule poster

What’s on the The Chain Rule poster?
The rule, 3 worked examples, and the mistake everyone makes. The derivative of a composition is the outer derivative at the inner function, times…; d/dx f(g(x)) = f′(g(x)) · g′(x); d/dx sin(3x²) = 6x cos(3x²); d/dx e^(−x²) = −2x e^(−x²); d/dx (ln x)⁵ = 5(ln x)⁴ / x; Common mistake: d/dx sin(3x) = cos(3x) → d/dx sin(3x) = 3 cos(3x). In Leibniz form dy/dx = (dy/du)(du/dx). The u must be a genuine function of x for that cancellation to mean anything.
Who is the The Chain Rule poster for?
The Chain Rule 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 The Chain Rule poster?
Whenever the argument of a function is anything other than a bare x. A wall chart earns its place by being glanceable from where the work is happening, so The Chain Rule belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with The Chain Rule?
Derivative Rules, Fundamental Theorem and Implicit Differentiation sit alongside The Chain Rule in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Derivative RulesFundamental TheoremImplicit Differentiation
Is the The Chain Rule poster free to download and print?
Yes. The Chain Rule 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 The Chain Rule poster print at?
The Chain Rule 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 The Chain Rule loses nothing.Printing guide

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