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Help with differentiation?

0 votes
Can anyone help me differentiate these? Really confused, thanks!

a) (3x+2)/ root x
b) ((2 root x) - 1) / x
asked Nov 5, 2014 in CALCULUS by anonymous

2 Answers

0 votes

a) (3x + 2)/√x

= (3x + 2)(x-1/2)

= 3x1/2 + 2x-1/2

Differentiating with respect to x.

= 3[ (1/2)x1/2-1] + 2 [ (-1/2)x-1/2-1]

= (3/2) x-1/2 - x-3/2

Derivative of (3x + 2)/√x is  3/(2√x) - 1/(√x)3.

answered Nov 5, 2014 by david Expert
edited Nov 5, 2014 by david
0 votes

b) (2√x - 1)/x

Differentiating with respect to x.

Apply quotient rule in derivatives d/dx(u/v) = [vu' - uv']/v2

u = 2√x - 1, v = x

u' = 1/√x , v' = 1

d/dx[(2√x - 1)/x] = [ x(1/√x) - (2√x - 1)(1)]/x2

= (√x - 2√x + 1)x2

Derivative of (2√x - 1)/x (- √x + 1)/x2

answered Nov 5, 2014 by david Expert

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