<s>[INST] Differentiation - Power rule Find derivative of this function
$$g(t)=-3t(6t^4-1)^{4/3}$$
I have tried it till the answer:
$ -3t.\frac{4}{3} (6t^4 - 1)^{\frac{4}{3}-1} .\frac{d}{dt}(6t^4 -1)  $
$-3t x \frac{4}{3} (6t^4-1)^\frac{1}{3} ( 6X4 t^3 -0 ) $
$ -4t (6t^4 -1)^\frac{4}{3} (24t^3) $ 
$-96t(6t^4-1)^\frac{1}{3} $ 
However , I checked and saw that the answer is
$$-3(6t^4-1)^{1/3}(38t^4-1)$$
I just started learning differentiation, and I don't understand my mistake on why I can't achieve the answer. Thanks!
 [/INST] after the product and the chain rule we get
$$-3(6t^4-1)^{4/3}-3t\frac{4}{3}(6t^4-1)^{1/3}\cdot 24t^3$$
after simplifying this derivative we get
$$-3 \sqrt[3]{6 t^4-1} \left(38 t^4-1\right)$$
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