Question

differentiate from first principle √x +(1/√x)​

Answer 1

Step-by-step explanation:

principle?

What is differentiation of y=log (√x+1/√x)?

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

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

dy/dx=lim h->0[f(x+h)-f(x)]/h.

=lim h->0 [(x+h)^1/2+1/(x+h)^1/2 - x^1/2–1/x^1/2]/h.

= lin h->0[{(x+h)^1/2- x^1/2}-{1/x^1/2–1/(x+h)^1/2}]/h.

=lim h->0[{(x+h)^1/2-x^1/1}-{(x+h)^1/2-x^1/2}/x^1/2.(x+h)^1/2]/h.

=lim h->0{(x+h)^1/2-x^1/2}[1–1/x^1/2 .(x+h)^1/2]/h.

Multiply above and below by{(x+h)^1/2+x^1/2}.

=lim h->0 {h}[1–1/x^1/2.(x+h)^1/2]/h×1/{(x+h)^1/2+x^1/2}.

=[1–1/x^1/2.x^1/2]×1/{x^1/2+x^1/2}.

=[1–1/x]×1/2x^1/2.

=1/2x^1/2 - 1/2x^3/2 , Answer.

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