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Need help finding derivative.?

0 votes
x^3 - 1 / (3x-1)^2.

I would prefer it if you used the quotient rule to solve.
asked Mar 11, 2013 in CALCULUS by linda Scholar

1 Answer

+1 vote

d /dx [X3- 1 / (3x - 1)2]

Put X3-1 = f(x) and (3x -1)2 = g(x)

Derivative  each side with  respective x

Therefore 3x2dx = f1(x)dx  and 2(3x - 1)3dx = g1(x)dx

Simplify

f1(x)dx= 3x2dx  and g1(x)dx = 6dx ( 3x - 1)

Recall : d / dx [f(x)/g(x)] = [g(x)f1(x) - f(x)g1(x)] / [g(x)]2

Substitue

d / dx [x3 - 1 / (3x - 1)2]  = (3x - 1)2[3x2] - [(x3 - 1)6(3x -1)] / [(3x -1)2]2

Simplify

d / dx [x3 - 1/ (3x - 1)2] = (3x - 1) [ (3x - 1)3x2 - 6(x3 - 1) ] / (3x - 1)4

Simplify

d / dx [x3 - 1/ (3x - 1)2] = [ (3x - 1)3x2 - (x3 - 1)6 ] / (3x - 1)3

 Derivative of [ x3 - 1 / (3x - 1)2] = [ 3(3x - 1)x2 - 6(x3 - 1) ] / (3x - 1)3

answered Mar 11, 2013 by diane Scholar

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