Limit
f'(x) = lim h→0 (f(x + h) - f(x))/h
f(x) = xⁿ → f'(x) = nx^(n - 1)
•
f(x) = 2x³ - 4x² + 2
f'(x) = 6x² - 8x
f(x) = 1/2 x⁴ + 2/3 x³ - 4x + 1
f'(x) = 2x³ + 2x² - 4
f(x) = (3x - 2)(x + 4)
f(x) = 3x² + 10x - 8
f'(x) = 6x + 10
f(x) = u/v = (2x - 1)/(3x - 1)
f'(x) = (u'v - uv')/v²
f'(x) = (2(3x - 1) - 3(2x - 1))/(3x - 1)²
f'(x) = 1/(3x - 1)²
f(x) = u⁵ = (4x + 3)⁵
f'(x) = 5u⁴. u'
f'(x) = 5(4x + 3)⁴. 4
f'(x) = 20(4x + 3)⁴
f(x) = (2x² - 3x + 1)⁴
f'(x) = 4(2x² - 3x + 1)³ . (4x - 3)
f'(x) = (16x - 12)(2x² - 3x + 1)³
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Limit
f'(x) = lim h→0 (f(x + h) - f(x))/h
f(x) = xⁿ → f'(x) = nx^(n - 1)
•
f(x) = 2x³ - 4x² + 2
f'(x) = 6x² - 8x
•
f(x) = 1/2 x⁴ + 2/3 x³ - 4x + 1
f'(x) = 2x³ + 2x² - 4
•
f(x) = (3x - 2)(x + 4)
f(x) = 3x² + 10x - 8
f'(x) = 6x + 10
•
f(x) = u/v = (2x - 1)/(3x - 1)
f'(x) = (u'v - uv')/v²
f'(x) = (2(3x - 1) - 3(2x - 1))/(3x - 1)²
f'(x) = 1/(3x - 1)²
•
f(x) = u⁵ = (4x + 3)⁵
f'(x) = 5u⁴. u'
f'(x) = 5(4x + 3)⁴. 4
f'(x) = 20(4x + 3)⁴
•
f(x) = (2x² - 3x + 1)⁴
f'(x) = 4(2x² - 3x + 1)³ . (4x - 3)
f'(x) = (16x - 12)(2x² - 3x + 1)³