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Palomaalves05
@Palomaalves05
May 2020
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Calcule a derivada das funções abaixo a) f(x)= e2x²+3x b) f(x) = (x3)/(x3-3) c) f(x) = 2sen(3x²+5)
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williammendes11
A)
f(x)= e^(2x²) + 3x
f'(x) =
e^(2x²).4x + 3
f'(x) = 4 e^(2x²) x + 3
(e^x)' = (e^x) . x'
b)
f(x) = (x³) / (x³ - 3)
f'(x) = [(3x² . (x³ - 3)) - (x³ . 3x²)] /
(x³ - 3)²
f'(x) = [(3x^5 - 9x²) - (3x^5)] / (x³ - 3)²
f'(x) = -9x² / (x³ - 3)²
(u/v)' = (u'v - uv') / v²
c) f(x) = 2 sen
(3x² + 5)
f'(x) = 2 cos (3x² + 5) 6x
f'(x) = 12x cos
(3x² + 5)
(sen u)' = cos u
(;
4 votes
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f'(x) = e^(2x²).4x + 3
f'(x) = 4 e^(2x²) x + 3
(e^x)' = (e^x) . x'
b) f(x) = (x³) / (x³ - 3)
f'(x) = [(3x² . (x³ - 3)) - (x³ . 3x²)] / (x³ - 3)²
f'(x) = [(3x^5 - 9x²) - (3x^5)] / (x³ - 3)²
f'(x) = -9x² / (x³ - 3)²
(u/v)' = (u'v - uv') / v²
c) f(x) = 2 sen (3x² + 5)
f'(x) = 2 cos (3x² + 5) 6x
f'(x) = 12x cos (3x² + 5)
(sen u)' = cos u
(;