Math Problem Statement
y=sin^2x then d^ny/dx^n
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Differentiation
Chain Rule
Higher-Order Derivatives
Formulas
y = sin^2(x) = (sin(x))^2
dy/dx = 2sin(x) * cos(x) = sin(2x)
nth derivative formula: d^n y/dx^n = 2^k * sin(2x) (odd n), 2^k * cos(2x) (even n)
Theorems
Chain Rule
Trigonometric Identities (sin(2x), cos(2x))
Generalization of nth derivatives of trigonometric functions
Suitable Grade Level
Undergraduate