Find dy/dx?

Question

Of (x-1)sqrt(6-x) 

Answer 1

The function f(x) = (x - 1)√(6 - x)

Apply derivative on each side with respect of x.

f'(x) = d/dx [(x - 1)√(6 - x)]

Apply product rule in derivatives.

d/dx (uv) = uv' + vu'

u = x - 1, v = √(6 - x)

u' = 1, v' = -1/2(√(6 - x))

f'(x) = (x - 1)[-1/2(√(6 - x))] + [√(6 - x)](1)

f'(x) = [-(x - 1)/2(√(6 - x))] + √(6 - x)

f'(x) = [ -(x - 1) + 2(6 - x)]/[2√(6 - x)]

f'(x) = [ - x + 1 + 12 - 2x)]/[2√(6 - x)]

f'(x) = [ - 3x + 13]/[2√(6 - x)].