Differentiation of fractional and negative powers

[bob4000]

hello reader

i have a problem understanding the following type of equation.

(n+x)/nth root of x

n being a fixed numerical value and x being the unknown

how would i differentiate such a problem

an example of this is:

(1+x)/4th root x
thank you

 

[dextercioby]

U mean this

$$(x^{\frac{1}{4}})'=...?$$

If so,apply the rule for differentiating any power of "x"...

Daniel.

 

[bob4000]

the question reads 1+x/4th root of x

therefore to simplify this:

(1+x) divided by (x^1/4)

how do i get this fraction into a negative function of x

if this was 1 divided by 4th root of x i know that this is then 1/x^1/4
which is x^-1/4

however, when there is a '+x' involved, i get stuck. what do you do with the 1+x to differentiate

 

[dextercioby]

Aaa,that's something else.

$$[\frac{1+x}{x^{\frac{1}{4}}}]'=[x^{-\frac{1}{4}}(1+x)]'$$

Now differentiate like a product...

Daniel.

 

[HallsofIvy]

Or,and I think simpler, write $x^{-\frac{1}{4}}(1+x)= x^{-\frac{1}{4}}+ x^{\frac{3}{4}}$ and differentiate that.