Question

if y =(6x)raised to the power 1/2 then find the value of dy/dx. options are 1) root 6 x 2) x/root 6 3)root 6 /x 4)root 6 /2 root x...

Answer 1

given, y = (6x)^1/2

squaring both sides,

y² = 6x

now, differentiating with respect to x,

d(y²)/dx = d(6x)/dx .....(1)

using concept : if y = f(x)ⁿ is given then differentiation of y with respect to x, dy/dx = $nf(x)^{(n-1)}\frac{df(x)}{dx}$

so, now for d(y²)/dx = 2y^(2 - 1) × dy/dx

= 2y dy/dx

and d(6x)/dx = 6 × dx/dx = 6

from equation (1),

2y dy/dx = 6

or, dy/dx = 3/y

putting value of y = (6x)½

so, dy/dx = 3/√(6x) = (√6)/(2√x)

hence, option (4) is correct choice.