Question

Find the derivative: y = square root of x(x+14).

The square root is only on the x. Please show work and explain. I don't know how to do this. Thanks!

Answer 1

if y = √u = u^(1/2)
y' = 1/2 * u^(-1/2) u'

u = x^2+14x
u' = 2x+14

y' = (2x+14)/(2√x(x+14))
= (x+7)/√x(x+14)

Answer 2

oops. I didn't read it carefully

use the product rule: if
y = f*g, y' = f'*g + f*g'

y = (x+14)√x
y' = (1)√x + (x+14)*(1/2√x)
= (2x+x+14)/2√x
= (3x+14)/2√x