Derivatives Polynomial

Question

anonymous · Answer

$$f(x)=\frac{ 2x^2+3x+2 }{ sqrtx}$$

anonymous · Answer

f`(x)

anonymous · Answer

$$f(X)=(2x^+3x+2)(x^\frac{ -1 }{ 2 })$$
Product rule.

zehanz · Answer

If you write  1/sqrt(x) as x^(-1/2), you can multiply and then differentiate term by term:$$f(x)=(2x^2+3x+2) \cdot x^{-\frac{1}{2}}=2x^{\frac{3}{2}}+3x^{\frac{1}{2}}+2x^{-\frac{1}{2}}$$So$$f'(x)=3x^{\frac{1}{2}}+\frac{3}{2}x^{-\frac{1}{2}}-x^{-\frac{3}{2}}$$Of course, you now have to rewrite this formula with radicals again and ideally write it as one fraction...

anonymous · Answer

mmm, why its x^-1/2?

zehanz · Answer

sqrt(x)=x^(1/2), but you are dividig by it, so you multiply with 1/ x^(1/2) = x^(-1/2)

anonymous · Answer

I see! could you tell me the rule? i am missed up! theres so many rules and i get to confuse which one is to apply

zehanz · Answer

Do you mean $$a^{-b} = \frac{1}{a^b}$$?

anonymous · Answer

No, derivative rule? I am not sure what its called

zehanz · Answer

Power Rule:$$\left( x^n \right)' =nx^{n-1}$$It applies for non-integer n as well.

anonymous · Answer

I am still confused.
say f(x)=4+5/x+(3/x^2)
f'(x)=
I divide it by x^2? then do nx^n-1?

zehanz · Answer

f(x)=4+5x^(-1)+3x^(-2)
f'(x)=(-1)5x^(-2)+ (-2)3x^(-3)=...

anonymous · Answer

Oh I finally got it, I was confused with limits. :)

zehanz · Answer

Hope it helped!

anonymous · Answer

absolutely you helped me a lot! 
:)

zehanz · Answer

YW!