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

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Answer 1 · 2017-01-13T18:57:08

$176/81 x^10 -32/3 x^8 +56/3 x^6 -40/3 x^4 +3x^2$

Expand the expression as

$x^3 [ (2/3 x^2)^4 +4 (2/3 x^2)^3 (-1) +6 (2/3 x^2)^2 (-1)^2 +4(2/3 x^2) (-1)^3 +(-1)^4]$

= $16/81 x^11 -32/27 x^9 +24/9 x^7 -8/3 x^5 +x^3$

Its first derivative would be

$176/81 x^10 -32/3 x^8 +56/3 x^6 -40/3 x^4 +3x^2$

Alternatively, product rule of differentiation can also be used.

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