HPCCC Derivatives - Power Rule

f'(x) = x³ + x² - x

f'(x) = 4x³ + 12x² + 4x

f'(x) = 4x + 12x - 4x

f'(x) = 4x³ + 12x² - 4x

$$f'\left(x\right)=\frac{1}{2x}$$  

$$f'\left(x\right)=-2x^3$$  

$$f'\left(x\right)=2x$$  

$$f'\left(x\right)=-\frac{2}{x^3}$$  

g'(x) = 1 - 2x

g'(x) = -2x

g'(x) = -2

g'(x) = -1

1

Not 0

0

The coefficient in front of x

$$f'\left(x\right)=-9x^2-11x+4x-80$$

$$f'\left(x\right)=-9x^2-22x+4x$$

$$f'\left(x\right)=-9x^2-22x+4$$

$$f'\left(x\right)=-27x^2-11x+4$$

h'(x) = 5x^2/3 - x^-5/6 + 3

h'(x) = 3x^2/3 - 6x + 3

h'(x) = 5x^4/3 - 6x + 3

h'(x) = 3x^4/3 - x^-5/6 + 3

16x³ - 21x² + x

6

16x³ - 21x² + 0.5x - 9

-4

y' = 8x + 3 -12x^-3

$$y'=8x+3+\frac{12}{x^3}$$

$$y'=8x+3-\frac{12}{x^3}$$

$$y'=8x+3+\frac{12}{x}$$

y+1=2(x+1)

y=2x-1

y=2x+2

y= -x-1