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Calculus - Derivatives Flashcards | StudBud

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Find f ' (x) of x2 = 6x2y..........

Find f ' (x) = (5x2 - 8x)4

Calculus - Derivatives

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Questions 9

Answers

1
Find f ' (x) = (5x² - 8x)⁴
f ' (x) = 4(5x2 - 8x) (10x2 - 8)
f ' (x) = 4(5x2 - 8x)3 (10x - 8)
f ' (x) = 4(5x2 - 8x3) (10x - 8)
f ' (x) = (40x - 32)(5x2-8x)3
2
Find f ' (x) of x²= 6x²y..........
f ' (x) = (2x - 12xy) / (6x2)
f ' (x) = (6x - 14xy) / (3x2)
dy / dx = (2x - 12xy) / (6x2)
f ' (x) = (x - 6xy) / (3x2)
3
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4
Find the first derivative of f(x) = 5x³ + ¾x² + 3x^½
f '(x) = 15x2 + 3/2x + 3/2x-½
f '(x) = 15x2 + 6/4x + 3/2x½
f '(x) = 15x2 + 6/4x + 3/2x-½
f '(x) = 15x2 + 3/2x + 3/2x½
5
Using Calculus how could you find Acceleration??????????
d2y / dx2
dy / dx
f ''' (x)
Find f ' (x)
6
Find dy / dx of 3y² = 2x² + 2x
dy / dx = (4x + 2) / (6y)
6y (dy / dx) = 4x + 2
dy / dx = (2x + 1) / (3y)
7
A particle of a curve is modeled by f(t) = 5t³- 3t² + 14t. Determine acceleration at 4 mins.
f '' (t) = 30t- 6
120 m/m2
114 m/m2
f ' (t) = 15t2- 6t + 14
8
FInd d²y / dx² of y = 2x⁴ - 8x³ + 2x
y"=8x3- 24x2 + 2
y"=24x2 + 48x + 2
y"=24x2 + 48x
y"=24x2 - 48x
9
The Defintion of a Derivative starts with the limit of 'h' going to 0 and then.................
f ' (x) = ( f(x+h) - f( x ) ) / (h)
f ' (x) = ( f(x + h) - f(x) ) / ( (x + h) - x )
f ' (x) = f(x) - ( f(x + h) - f(x) ) / ( (x + h) - x )