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酷庄稼糸油油油油油油油油油油油庄韓: y=2x3
sinx
Product and quotient rules
Bytheendofthelessonyouwillbeableto:
 Usetheproductandquotientrulestofindthe
derivativeoffunctions.
Iff(x)=u(x).v(x)then
f'(x)=u'(x).v(x)+u(x).v'(x)
simpler: (uv)'=u'v+uv'
The product rule
酷庄稼糸油油油油油油油油油油油庄韓: y=2x3
sinx
酷庄稼糸油油油油油油油油油油油庄韓:
酷庄稼糸油油油油油油油油油油油庄韓:
酷庄稼糸油油油油油油油油油油油庄韓:
酷庄稼糸油油油油油油油油油油油庄韓:
Find fory=ex
sinx
The quotient rule
If then:
simpler:
2
酷庄稼糸油油油油油油油油油油油庄韓:
酷庄稼糸油油油油油油油油油油油庄韓:
酷庄稼糸油油油油油油油油油油油庄韓:
酷庄稼糸油油油油油油油油油油油庄韓:
Differentiate with respect to x:
酷庄稼糸油油油油油油油油油油油庄韓:
酷庄稼糸油油油油油油油油油油油庄韓:
Findtheequationsofthetangentlinetothecurve
y=xcosxatthepointwherex=.
Thefunctionhasa
horizontaltangentlineatx=k.Findk.
Findthecoordinatesofthetwopointsonthecurve
y=sinx(2cosx+1),intherange
wherethegradientis
Findthecoordinatesofthestationarypointsonthe
curve intherange0x2.
Findandclassifythestationarypointsonthecurve
y=x2
ex
.Hencesketchthecurve.
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