Alice_Dump
Ppl of the world.. here comes the Next question -..-
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Alice_Dump
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its about the definition of the derivative >>>
SmithsAccount
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were all beaming with anticipation...
Alice_Dump
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Apply the definition of the d derivative to compute \[f \prime (x) \] where \[f(x)=3x ^{2}+x-2\]
rvgupta
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6x+1
AravindG
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6x+1
Alice_Dump
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i know .. \[f'(x)= 6x +1\] .. but my teacher said do it with details like long way to get this answer
Alice_Dump
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-..- i don't know how
AravindG
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i see well
|dw:1349804778192:dw|
Alice_Dump
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XD ur hand-writting is Funnie XP
AravindG
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2
lim delta x tends to 0
SmithsAccount
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ikr!
Alice_Dump
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O_O sorry didn't mean to .. oops im sorry >> >_< sowwie
amorfide
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you have a function of x
F(X)=3x²+x−2
to differentiate you multiply the coefficient of the unknown by the power of the unknown and decrease the power of the unknown by 1
for example
f(x)=x²
f'(x)=2(1)x^2-1=2x
so
f(x)=x
f'(x)=1(1)x^1-1=x^0=1
if you have
f(x)=2x²
f'(x)=2(2)x^2-1=4x
does this help?
|dw:1349804820461:dw|
AravindG
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np @Alice_Dump did u get that ?
Alice_Dump
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-..- ppl brb .. gemme 5 minutes i need to do something .
Alice_Dump
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wait okie >_<
UnkleRhaukus
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\[f'(x)=2\times 3x^{2-1} +1\times x^{1-1}-0\times2x^{0-1}=6x +1\]
rvgupta
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2*3x^(2-1)+x(1-1)
anonymous
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\[f(x)=3x^2+x-2\]
\[f(x+h)=3(x+h)^2+(x+h)-2=3(x^2+2xh+h^2)+x+h-2\]
\[=3x^2+6xh+3h^2+x+h-2\]
\[f(x+h)-f(x)=3x^2+6xh+3h^2+x+h-2-(32x^2+x-2)\]
\[=6xh+h+3h^2\]
rvgupta
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2 being constant will disappear
anonymous
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divide by \(h\) and get
\[\frac{f(x+h)-f(x)}{h}=6x+1+3h\] take the limit as \(h\to 0\) get \(6x+1\)
anonymous
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you needed it done by hand right? not power rule
it is a bunch of algebra, that is all
only last step is calc, and that is taking the limit by replacing \(h\) by \(0\)
AravindG
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indeed @satellite73 has illustrated the given problem nicely with the formula i have given you ...i think that clears evrything
anonymous
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question said "Apply the definition of the derivative to compute"
anonymous
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@AravindG thanks
AravindG
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yw :)
Alice_Dump
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:} back ..
Alice_Dump
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i got the question now :] thnx ppl ^_^'
Alice_Dump
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heehehe