Differentiation?

Question

Differentiate the function.

y = sqrt(x)(x-1)

Answer 1

y = (x^1/2) (x-1)

dy/dx = (x^1/2)(1) + (1/2)(x^-1/2)(x-1)

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

= (3/2 x^1/2)(1-1/3x^-1)

Answer 2

Hi,
Use the product rule, of course.
y=√(x)(x-1)
y’ = x^(1/2)(x-1) (Convert to exponential.)
= x^(1/2)(1) = (x-1) ((1/2)x^(-1/2)
=x^(1/2) + (x-1)/(2√x) (Eliminate negative exponent.)
=[(2x^(1/2) x^(1/2) + (x-1)]/(2√x) (Multiply by least common denominator.)
= (2x +x-1)/(2√x) (Add exponents in multiplication.)
=(3x-1)/(2√x) (Add like terms.)

Hope this helps.
FE