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Differentiation – Power Rule

Q:  Find d/dx f(x) if f(x)=3x^2.


A:  Find d/dx is telling us to find the derivative, also known as f'(x).

Therefore, if:

f(x) = 3x^2

f'(x) = 2*3x = 6x.

How do I know this?  The power rule.  The power rule tells us to bring the power (or exponent) down in front as a multiplier, and subtract 1 from it:

f(x) = 3x^2 [bring the “2” down in front as a multiplier and subtract 1 from it]

f'(x) = 2 * 3x^(2-1) = 6x^1 = 6x.

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