Differentiate the function

Question

Differentiate the function:

 

(x² + 2√( x³)) / (4√x)

 

 

ANSWER: 3/8 x^1/2  + 1/2

practice exam q #11

Answer 1

Hi Mia,

 

You could use the quotient rule as the function is expressed initially, but easier to separate into two separate fractions.

 

f(x) = x²/4x^1/2 + 2x^3/2/4x^1/2

f(x) = 1/4 x^3/2 + 1/2 x¹

 

Now f'(x) = (1/4)(3/2)x^1/2 + 1/2 = 3/8 x^1/2 + 1/2