Question

differentiate x^2/3 using first principle​

Answer 1

Step-by-step explanation:

x^2/3

x2 divide by 3

yes this is the correct differntiate between both of them

Answer 2

Answer:

Let y = x^-3/2…………(1)

Let Δx be a small change in x. Let the corresponding change in y be Δy

Then y + Δy = (x+Δx)^-3/2………..(2)

(2)-(1) gives Δy = (x+Δx)^-3/2 - x^-3/2

Dividing by Δx, we have Δy/Δx = {(x+Δx)^-3/2 - x^-3/2}/Δx

Δy/Δx = {(x+Δx)^-3/2 - x^-3/2}/{x+Δx)-x}

As Δx->0 RHS which is of the form (x^n - a^n)/(x-a) that tends to n a^n-1 as x->0

Hence dy/dx = (-3/2) x^(-3/2 -1) = (-3/2) x^(-5/2)

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