Differentiate the function. Y= √x(x-4) ?

The answer is #(3x-4)/(2sqrtx)# but I'm not sure how to get that answer?

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1 Answer
Max G.
Feb 14, 2018

Start by using the distributive property.

Explanation:

Let #y = sqrtx(x - 4)#
Then #y = xsqrtx - 4sqrtx = x^(3/2) - 4x^(1/2)#
Differentiate using the power rule.
#dy/dx = (3/2)x^(1/2) - 2x^(-1/2)#
# = (3/2)x^(1/2) - 2/x^(1/2)#
# = (3sqrtx/2) - 2/sqrtx#
Get a common denominator of #2sqrtx#, and
you'll arrive at their answer.

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