Differentiate?

Question

a) x^2 - 5x + 2/ 4x

Please explain how you do it

Answer 1

Quotient Rule

[(2x-5)(4x) - (4)(x^2-5x+2)] / 16x^2

Simplify that if you want.

Quotient Rule:

f(x) / g(x) = h(x)

h'(x) = [f'(x)*g(x) - g'(x)*f(x)] / [g(x)]^2

Answer 2

Use power rule on 1st 2 terms and quotient on last term.
2x -5 -8/16x^2
= 2x - 5 -1/(2x^2)

Answer 3

quotient rule:

d/dx (u/v) = (u'v - v'u) / v^2

[d/dx (x^2 - 5x + 2) (4x) - d/dx (4x) (x^2 - 5x + 2) ] / (4x)^2

[ (2x - 5) (4x) - 4(x^2 - 5x + 2) ] / (16x^2)

(8x^2 - 20x - 4x^2 + 20x - 8) / (16x^2)

(4x^2 - 8) / (16x^2)

4 (x^2 - 2) / (16x^2)

(x^2 - 2) / (4x^2) <== answer