Unit 2 Calculus AB

Using Definition of Derivative

100

Using the definition of derivative formula, solve for v'(t):

V(t)=3−14t

v'(t) = -14

200

Using the definition of derivative formula, solve for q'(t):

Q(t)=10+5t−t²

q'(t) = 5 - 2t

300

 Using the definition of derivative formula, solve for z'(t):

Z(t)=√(3t-4)

z'(t) = (3) / (2√(3t-4))

400

 Using the definition of derivative formula, solve for f'(x)

f(x) = 10x³ + 36x² - 8x +2

f'(x) = 2(15x² + 36x - 4)

Product/Quotient/Chain

100

Solve for f'(x):

f(x) = x³(2x² + 1)

f'(x) = 10x⁴ + 3x²

200

Solve for g'(x):

g(x) = (x² + 1) / (x² - 1)

g'(x) = (-4x) / ((x² - 1)²)

300

Solve for f'(x)

f(x) = [(x² - 4)/(x - 1)] x [(x² - 1)/(x + 2)] v

f'(x) = 2x - 1

400

Solve for h'(x)

h(x) = (√(2x +5)) / (x - 3)

h'(x) = -(x + 8) / (√ (2x + 5) (x - 3)²)

Trig Functions

100

Solve for f'(x):

f(x)= 3tanx

f'(x) = 3secx^2

200

solve for f'(x):

f(x) = 14tanx(cosx) + 10cscx

f'(x) = 14cosx - 10cscxcotx

300

solve for f'(x)

f(x) = (x⁵) / (4sinx)

f'(x) = (x⁴(5sinx - xcosx)) / (4sin²x)

400

solve for f'(x)

f(x) = 10cos³(4x)

f'(x) = -120cos²(4x)sin(4x)

Natural Log and Exponential Functions

100

Solve for f'(x)

f(x) = x²e^x

f'(x) = 2xe^x + x²e^x

200

Solve for f'(x)

f(x) = (10^x) / (ln 10)

f'(x) = 10^x

300

Solve for f'(x)

f(x) = ln√(5x-7)

f'(x) = 5 / (2(5x - 7))

400

solve for f'(x)

f(x) = ln ( (x² + 1) / (x³ - x) )

f'(x) = ((2x) / (x² + 1)) - ((3x² - 1) / (x³ - x))