Derivatives

Question

What is dy/dx if y = (4x^2)/(8+0.2x) ?

Answer 1

when given a function in the form F/G I always tell my students to speak like cave men and women.

 

Pronounce FG like "fugah"

 

So we say Fugah Fugah (now we sound like cave men and women)

 

Fugah Fugah Primes on the outside   (it's just a fun way of remembering the rule)

 

 

(F 'G - FG')/G²

 

Also for the product rule we also say fugah fugah 

 

F 'G+FG'

Answer 2

Ken, examine your function. Rename the numerator u and rename the denominator v, which are names of simpler functions of x.

 

Use the Quotient  Rule: (u/v)' = (u'v - uv') / v²

u' = 8x

v' = 0.2, a.k.a. 1/5

 

Substitute these four things [u, v, u' & v'] into the Quotient Rule formula's right-hand side, and that will be the derivative y'.  Generally, one them simplifies matters, using regular Algebra.

Answer 3

Ken

 

You need to use the quotient rule

 

denominator (d/dx numerator) - numerator (d/dx denominator)

-----------------------------------------------------------------------

                           denominator squared

 

[(8+0.2x)(d/dx 4x^2) - (4x^2)(d/dx 8+0.2x)]

----------------------------------------------------

                            (8+0.2x)^2

 

(8+0.2x)(8x) - (4x^2)(0.2)

-------------------------------

        (8+0.2x)^2

 

64x + 1.6x^2 - .8x^2          64x+1.6x^2

-------------------------  = ------------------

 64 + 3.2x + .04x^2        64+3.2x+0.4x^2