Calculus practice
Trigonometric Chain Rule worksheets
Differentiate bounded sine, cosine, tangent, cosecant, secant, and cotangent compositions in radians.
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Differentiate each function. Give each answer in exact factored form.
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Differentiate the outer operation, keep its original input, and multiply by the derivative of that input. Interpret angles in radians; arccot uses its principal range (0, pi).
Learning objective
What this activity builds
Apply the Chain Rule to exact trigonometric and inverse-trigonometric compositions.
Worked example
Differentiate y = sin(3x).
dy/dx = 3cos(3x)
Differentiate the outside function, then multiply by the derivative of its input.
Teaching notes
Make the practice count
- Name the inner expression before differentiating.
- Keep exact factors rather than expanding.
- Check the original real domain and the stricter derivative-formula domain.
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Choose 8, 10, or 12 problems, any of the six functions, outside or inside placement, and prime, Leibniz, or mixed notation.