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# functions watch

1. how do i find and simplify an expression for f'(x) when f(x)=(x^2 +3)/(4x+1)

thanks
2. (Original post by sarah12345)
how do i find and simplify an expression for f'(x) when f(x)=(x^2 +3)/(4x+1)

thanks
Use the quotient rule?
3. (Original post by Gaz031)
Use the quotient rule?
or the product rule:

f(x) = (x² +3)(4x+1)^-1
4. As above, apply the quotient rule

f'(x)=(u/v)'=((vu'-uv')/v²)

Let u=x²+3=>u'=2x

AND

Let v=4x+1=>v'=4

=>f'(x)=((2x(4x+1)-4(x²+3))/(4x+1)²)

=>f'(x)=2((2x-3)(x+2)/(4x+1)²)

Newton.
5. Yet another method:

f(x)
= (x^2 + 3)/(4x + 1)
= [(1/4)x(4x + 1) - (1/4)x + 3] / (4x + 1)
= [(1/4)x(4x + 1) - (1/16)(4x + 1) + 49/16] / (4x + 1)
= (1/4)x - (1/16) + (49/16)/(4x + 1)

The differentiation is now easy.

f'(x) = (1/4) - (49/4)/(4x + 1)^2

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