# How do you use the quotien rule to differentiate #1/ (3x^2+2)^3#?

##### 1 Answer

#### Explanation:

If you are studying maths, then you should learn the Quotient Rule for Differentiation, and practice how to use it:

# d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 # , or less formally,# (u/v)' = (v(du)-u(dv))/v^2 #

I was taught to remember the rule in word; " *vdu minus udv all over v squared* ". To help with the ordering I was taught to remember the acronym, VDU as in Visual Display Unit.

We will need to differentiate the denominator (using the chain rule), so let's do that first :

# d/dx(3x^2+2)^3 = 3(3x^2+2)^2(6x) #

# :. d/dx(3x^2+2)^3 = 18x(3x^2+2)^2 #

So with

# dy/dx = ( ((3x^2+2)^3)(d/dx(1)) - (1)(d/dx(3x^2+2)^3) ) / ((3x^2+2)^3)^2 #

# :. dy/dx = ( 0 - 18x(3x^2+2)^2 ) / (3x^2+2)^6 #

# :. dy/dx = (- 18x) / (3x^2+2)^4 #