Test review please help

Question

Answer 1

(4)

f(x) = x√(2x - 3) .

Rewrite the expression f(x) = √[x² (2x - 3) ] .

f(x) = √[ 2x³ - 3x² ] 

Apply derivative with respect to x on each side .

Answer 2

(5)

The function p(x) = g²(x) .

Apply derivative with respect to x on each side .

p'(x) = 2g(x) [g'(x)]

Now substitute x = 3 in the above equation .

p'(3) = 2g(3) [g'(3)] 

p'(3) = 2(2) [3]                           [Given g(3) = 2 and g'(3) = 3 ]

p'(3) = 12 

Hence p'(3) = 12  .

Answer 3

(6)

The function .

Apply derivative on each side with respect to x .

Apply quotient rule of derivatives  .