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