What is the derivative of #(4-x)/x^(1/3)(6-x)^(2/3)#?

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Answer 1 · 2016-11-22T01:23:02

Ew. If we assume that function is #f(x)#

#f'(x) = (4x^2−16x−24)/(3*(6-x)^(1/3)x^(4/3)#

Break up the equation and tackle it piece by piece.

I'll let you do the calculations but i'll simplify how it looks:

Let #a=(4-x) #
Let #b=(x^(1/3)) #
Let #c=(6-x)^(2/3) #

#f'(a/b) = [[d/dx(a) * (b)] - [d/dx(b) * (a)]]/b^2 #

Then use the product rule to finish it.

#f'(x) = f'(a/b) * (c) + (a/b) * d/dx(c) #