How do you use the chain rule to differentiate #y=(x+1)^6/(3x-2)^5#?
1 Answer
Mar 9, 2017
You avoid the quotient rule, and take the derivative using the product rule. The chain rule states:
#(df)/(dx) = (df)/(dy)(dy)/(dx)#
So, you incorporate the nested function, and take the derivative of that function as well.
#color(blue)((dy)/(dx)) = (x+1)^6 * d/(dx)[1/(3x-2)^5] + 1/(3x-2)^5*d/(dx)[(x+1)^6]#
#= (x+1)^6 * -(5)/(3x-2)^6*d/(dx)[3x-2] + 1/(3x-2)^5 * 6(x+1)^5 * d/(dx)[x+1]#
#= color(blue)(-(15(x+1)^6)/(3x-2)^6 + (6(x+1)^5)/(3x-2)^5)#
