d/dx(X^4)
= 4X^3 ( first derivative )
d/dx(4X^3)
= 12X^2 ( second derivative )
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2x
f(x) = 3x4 - 2x2 + 7f ' (x) = 12x3 - 4xf ' ' (x) = 36x2 - 4
1 divided by x to the third power equals x to the negative third. The derivative of x to the negative third is minus three x to the negative fourth.
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
The first derivative of e to the x power is e to the power of x.