Unit 4 Project

Power Rule

100

f(x)=5x^-3

f'(x)=-15x^-4

300

f(x)=13x^1/2+2x

f'(x)=6.5x^-1/2+2

500

f(x)=12x³+4x

f(x)= 36x²+4

Product Rule

100

f(x)=(5x²+7)(8x-5)

f'(x)=120x²-50x+56

300

f(x)=(6x³-12x²)(4x⁴+12x^-3)

(6x³-12x²)(16x³-36x^-4)+(4x⁴+12y^-3)(18x²-24x)

500

f(x)=(16x²-14x)(15x^-3+12-4x⁴)

(16x²-14x)(-45x^-4-16x³)+(15x^-3+12-4x⁴)(36x-14)

Quotient Rule

100

f(x)=(x³-4x)/(3x)

(3x)(3x²-4)-(x³-4x)(3)/(3x)²

300

f(x)=(6x⁴-12x²)/(14x-3)

(14x-3)(24x³-24x)-(6x⁴-12x²)(14)/(14x-3)²

500

f(x)=(x)/(12x^-3+4x²)

(12x^-3+4x²)(1)-(x)(-36x^-4+8x)/(12x^-3+4x²)²

Exponential/Logarithmic Rule

100

f(x)=e^x-3, determine if there is a horizontal tangent.

1

300

f(x)=lnx-14x+e^x, find f'(x)=2

-13.5+e²

500

f(x)=3ln(x³-3), determine the rate of change at x=4

3/61

Chain Rule

100

f(x)=2sin(cosx)

F(x)=2cos(cosx) * -sinx

300

f(x)=e^2x-3

e^2x-3 * 2

500

f(x)=(3x²-4)²

2(3x²-4) * 6x