Collaborative Activity

Basic differentiation rules

100

s(t) = t³+5t²-3t+8

s´(t) = 3t²+10t-3

200

f(t)= -2t²+3t-6

f´(t)= -4t+3

300

f(x)= 4/x⁵

f´(x)= -20/x⁶

400

y= (4x²-5)(2x³+7x)

y´= 40x⁴+54x²-35

500

f(t)= t⁴-3 / 2t⁵+1

f´(t)= -2t⁸+30t⁴+4t³ / (2t⁵+1)²

Product o Quotient Rule

100

Product Rule:

f(x)=(-2x²+25)(x⁵-1)

-14x⁶+125x⁴+4x

200

Quotient Rule:

y= x²-1 / x+2

x²+4x+1 / (x+2)²

300

Product Rule:

f(x)=(-3x³+10)(x²-6)

-15x⁴+54x²+20x

400

Quotient Rule:

y= 5x²-6 / x-3

5x²-30x+6 / (x-3)²

500

Product Rule: 

(-7x⁴+10x^2/5+8)(x²+10)

-42x⁵-280x³+24x^7/5+16x+40/x^3/5

Chain Rule

100

y= (x⁴-5)²

y´= 8x⁷-40x³

200

y= 1 / x+2

y´= -1 / (x+2)²

300

f(x)= (6x²+7x)⁴

f´(x)= (48x+28)(6x²+7x)³

400

f(x)= ln(√x³-3)

f´(x)= 3x² / 2x³-6

500

f(z)= ³√1-8z

f´(z)= -8/3 (1-8z)^-2/3

Rules for exponential or logarithm functions

100

y= 5^3-2x

y´= -2ln5(5^3-2x)

200

y= e^2x-4-3x²

y´= 2e^2x-4-6x

300

f(x)= x / ln(x)

f´(x)= ln(x)-1 / ln(x)²

400

y= ln(4x√6x +1)

y´= 144x²-6√6x / 96x³-1

500

y= 5log₂(3-x²)

y´= - 10x / ln(2)(3-x²)

Rules for trigonometric functions

100

f(x)= sen²(8x)+cos²(8x)

f´(x)= 0

200

y= tan(9x)

y´= 9sec²(9x)

300

f(x)= sin(e^2x-5)

f´(x)= 2e^2x-5cos(e^2x-5)

400

y= (1-sin²x)(1+tan²x)

y´= 0 

500

y= 8cos(x²-1)

y´= -16xsin(x²-1)