use two strategies to differentiate the function

[wind]

f(x) = (3x^2 +1) ( x + 1 ) / x^2 + 2x +1

f(x) = (3x^2 +1) ( x + 1 ) / ( x + 1 ) ( x + 1 )
f(x) = (3x^2 +1) / ( x + 1 )

fprime (x) = ( 6x )( x + 1 ) + ( 3x^2 + 1 )( 1)
= 6x^2 + 6 + 3x^2 + 1
= 9x^2 + 7

Is this right?


for the other way could I do this?

f(x) = (3x^2 +1)( x^-1 + 1 ^-1)


Thanks.

 

[galactus]

Quotient rule, wind, quotient rule.

\(\displaystyle \frac{3x^{2}+1}{x+1}\)

\(\displaystyle \L\\\frac{(x+1)(6x)-(3x^{2}+1)(1)}{(x+1)^{2}}\)

 

[skeeter]

for the other way could I do this?

f(x) = (3x^2 +1)( x^-1 + 1 ^-1)

product rule ...
f(x) = (3x² + 1)(x + 1)^-1

note ... (x + 1)^-1 does not equal x^-1 + 1^-1

 

[wind]

Quotient rule, wind, quotient rule.

I got confused...


Thanks, galactus, skeeter


How do I find the derivitive of (x + 1)^-1 if I don't know the Chain Rule?

 

[skeeter]

the chain rule is not needed in this case since the derivative of x + 1 is 1.

\(\displaystyle \L \frac{d}{dx}[(x + 1)^{-1}] = -1(x + 1)^{-2} = \frac{-1}{(x+1)^2}\)

 

[wind]

I got 3x^2 + 6x -1 / (x +1 ) ^2 is this right?

Thanks

 

[galactus]

Yep

 

[wind]

Thanks