Given the function $g (x) = 4 x^{3} + 6 x^{2} - 24 x$ , find the first derivative, $g^{'} (x)$ .
$g^{'} (x) =$

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$g^{'} (x) = 12 x^{2} + 12 x - 24$

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Step 1 ：The derivative of a function can be found by applying the power rule, which states that the derivative of $x^{n}$ is $n \cdot x^{n - 1}$ .

Step 2 ：Applying the power rule to the function $g (x) = 4 x^{3} + 6 x^{2} - 24 x$ , we get $g^{'} (x) = 3 \cdot 4 x^{3 - 1} + 2 \cdot 6 x^{2 - 1} - 24 \cdot x^{1 - 1}$ .

Step 3 ：Simplifying the above expression, we get $g^{'} (x) = 12 x^{2} + 12 x - 24$ .

Step 4 ：So, the first derivative of the function $g (x)$ is $g^{'} (x) = 12 x^{2} + 12 x - 24$ .

Step 5 ： $g^{'} (x) = 12 x^{2} + 12 x - 24$

Given the function g(x)=4x3+6x2−24x, find the first derivative, g′(x).g′(x)=

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Given the function $g (x) = 4 x^{3} + 6 x^{2} - 24 x$ , find the first derivative, $g^{'} (x)$ .
$g^{'} (x) =$