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SixBooks
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The function f: R → R is: f(x) =
(tan x) / (1 + ³√x) ; for x ≥ 0,
sin x ; for (-π/2) ≤ x < 0,
x + (π/2) ; for x < -π/2
_
For the interval (0,∞), we are interested in f such that
f(x) = (tan x) / (1 + ³√x) ; for x ≥ 0
f(x) = tan x / (1 + x¹ʹ³)
(1 + x¹ʹ³)•sec²x − tan x • (⅓ x ⁻²ʹ³)
f'(x) = ——————————————— ← by the quotient rule
(1 + x¹ʹ³)²
(1 + ∛x) sec²x − (tan x / (3 ∛(x²))
f'(x) = ——————————————— ← ANSWER
(1 + ∛x)²
OR
3x²ʹ³ (1 + x¹ʹ³)•sec²x − tan x
f'(x) = ————————————— ← ANSWER
3x²ʹ³ (1 + ∛x)²
>> From here I can't go any further...
Any help is more than welcome!
(tan x) / (1 + ³√x) ; for x ≥ 0,
sin x ; for (-π/2) ≤ x < 0,
x + (π/2) ; for x < -π/2
_
For the interval (0,∞), we are interested in f such that
f(x) = (tan x) / (1 + ³√x) ; for x ≥ 0
f(x) = tan x / (1 + x¹ʹ³)
(1 + x¹ʹ³)•sec²x − tan x • (⅓ x ⁻²ʹ³)
f'(x) = ——————————————— ← by the quotient rule
(1 + x¹ʹ³)²
(1 + ∛x) sec²x − (tan x / (3 ∛(x²))
f'(x) = ——————————————— ← ANSWER
(1 + ∛x)²
OR
3x²ʹ³ (1 + x¹ʹ³)•sec²x − tan x
f'(x) = ————————————— ← ANSWER
3x²ʹ³ (1 + ∛x)²
>> From here I can't go any further...
Any help is more than welcome!
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