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AP Calculus - Derivatives Review Flashcards | StudBud
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AP Calculus - Derivatives Review
AP Calculus - Derivatives Review
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1
What's the definition of a derivative?
y prime
lim as h--> 0 of (f(x+h)-f(x))/h
none of the above
lim as x-->a(f(x)-f(a))/(x-a)
2
Find the second derivative: f(x)=1/4x
2
-6x+2
f''(x)=-1/2x-6
f''(x)=1/2
f''(x)=1/12x3-3x2+2x
f''(x)=1/2x-6
3
The Quotient Rule: d/dx(u/v)=...
d/dx(u/v)=uv'+vu'
d/dx(u/v)=(vu'-uv')/v2
d/dx(u/v)=u'/v'
None of these
4
Find the first derivative: g(x)=√(5x+10)
g'(x)=(5/2)(5x+10)^-(1/2)
g'(x)=(5√(5x+10)/2)
g'(x)=5
g'(x)=√5x+√10
5
Find the first derivative: y=1/2
y'=1/4x2
y'=1/2
y'=0
y'=2
6
The Product Rule: d/dx(uv)=....
d/dx(uv) = u'v'
d/dx(uv)=f(x)
d/dx(uv)=u(dv/dx)+v(du/dx)
d/dx(uv)=uv'+vu'
7
Find the first derivative: x
2
-2xy+y=16
y'=(2y-2x)/(1-2x)
y'=2x
y'=16-x2-2xy
y'=0
8
Find the derivative: tan
-1
u
None of these
d/dx(tan-1u)=(1/√1-u2)(du/dx)
d/dx(tan-1u)=(-1/√1-u2)(du/dx)
d/dx(tan-1u)=(1/1+u2)(du/dx)
9
Find the first derivative: y=(x
3
-2x-3)
4
y'=3x2-2
y'=4(x3-2x-3)4(3x2-2)
y'=x3-2x-3
y'=4(x3-2x-3)3(3x2-2)
