Math Problem Statement
Differentiate the function using basic differentiation formulas. (a) f(x) = π 2 (b) f(x) = 3 4 x 8 (c) f(t) = 1.4t 5 − 2.5t 2 + 6.7 (d) y = sin(t) + π cos(t) (e) B(y) = cy−6 (f) y = x 5/3 − x 2/3 (g) y = √ x(x − 1) (h) S(R) = 4πR2 (i) g(u) = √ 2u + √ 3u (j) y = √ x+x x2 (k) f(θ) = sin(θ) 2 + c θ (l) f(t) = √3 t 2 + 2√ t 3
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Basic differentiation rules
Trigonometric differentiation
Product rule
Power rule
Chain rule
Formulas
d/dx(c) = 0 for constants
d/dx(x^n) = n*x^(n-1) for power functions
d/dx(sin(x)) = cos(x)
d/dx(cos(x)) = -sin(x)
Product rule: (uv)' = u'v + uv'
Chain rule: (f(g(x)))' = f'(g(x)) * g'(x)
Theorems
-
Suitable Grade Level
Grades 11-12 or early university calculus
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