What is the derivative of x^3 + 3/2 x^2 - sin (x) ?

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The rules for derivatives, is you bring the power down, and subtract 1 from the exponent. So, For example

f(x)=x^3

f'(x)= 3x^2

So we continue to do this for the first parts of the problem

3x^2+(2)(3/2)x

3x^2+3x

For the trig function -sin(x).

Well, cos(x)=-sin(x). Thus, the derivative -sin(x)=cos(x)

Thus the finished derivative is

3x^2+3x+cos(x).

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