AP Calc AB- Derivative Memorization Quiz

Constant Rule

d/dx ( c ) = 0

Power Rule

d/dx (xⁿ) = n * x^n-1

Constant Multiple Rule

d/dx (cxⁿ) = c * d/dx (xⁿ)

Sum/Difference Rule

d/dx (u ± v) = d/dx u ± d/dx v

Product Rule

d/dx (uv) = uv’ + vu’

The Quotient Rule

d/dx (u/v) = (vu’ - uv’) / (v²)

The Quotient Rule (words)

(low * d high - high * d low) / (low²)

d/dx (sinx)

cosx

d/dx (tanx)

sec²x

d/dx (secx)

secx * tanx

d/dx (cosx)

-sinx

d/dx (cotx)

-csc²x

d/dx(cscx)

-cscx * cotx

d/dx(e^x)

e^x

d/dx (ln x)

1/x

definition of derivative (equation)

f’(x) = lim (h→0) = (f(x+h) -f(x) )/ h

alternate definition of derivative (at a point)

f’(c )= lim(x→ c) (f(x) - f(c ))/ (x-c)

Where on a secant line does the derivative NOT exist?

Corner, Cusp, Vertical Tangent, Discontinuity/Step-Fuction

velocity graph = ?

derivative of position graph

acceleration graph = ?

second derivative of position graph/ derivative of velocity graph

Chain Rule

y’ (f(g(x)) = f’(g(x)) * g’(x)

Chain rule (verbal)

derivative of the outside, keep the inside, times derivative of the inside

d/dx sin^-1(x)

1/ (√1-x²)

d/dx sec^-1(x)

1/(lxl √1-x²)

d/dx tan^-1(x)

1/ (x²+1)

f’(x) = e^x

e^x

f’(x) = e^u

e^u * u’

f’(x) = a^x

a^x * ln(a)

f’(x) = a^u

a^u * ln(a) * u’

f’(x) = lnx

1/x

f’(x)= lnu

1/u * u’

f’(x)= loga(x)

1/(x*lna)

f’(x)=loga(u)

1/(u*lna) * u’