1 quick q (differentiate) (1 Viewer)

[d3vilz]

Differentiate:
f(x) = rootx - 1/rootx + 1

how do i get this as an answer 1/rootx(rootx + 1)^2 ????

thanks?

 

[shaon0]

Differentiate:
f(x) = rootx - 1/rootx + 1

how do i get this as an answer 1/rootx(rootx + 1)^2 ????

thanks?

sqrt(x)-1/sqrt(x) +1
=x^1/2 - x^-1/2
=1/2sqrt(x) + 1/2 x.sqrt(x)
=(x+1)/(2x.sqrt(x))
=1/(sqrt(x)(sqrt(x)+1)^2)

 

[bored of sc]

Differentiate:
f(x) = rootx - 1/rootx + 1

how do i get this as an answer 1/rootx(rootx + 1)^2 ????

thanks?

Quotient rule: f(x) = (vu'-uv')/v² where u is numerator and v is denominator.

So f'(x) = [(x<sup>1/2+1)*(1/2*x-1/2) - (x1/2-1)*(1/2*x-1/2)] / (x1/2+1)2 --- plug into formula, careful to put in correct numbers

= [(1/2 + 1/2*x-1/2) - (1/2 + 1/2*x-1/2)] / (x1/2+1)2 ---- expand topline, be sure to use your index laws like xa*xb = xa+b

= x-1/2 / (x1/2+1)2 ---- gather like terms and add subtract them etc

= 1/[x1/2*(x1/2+1)2] ---- move x-1/2 to the denominator so the index becomes positive

= 1/[root(x)*(root(x)+1)2] ---- change number indexes to square root signs</sup>

 

[d3vilz]

thanks shaon0 & bored of sc