Step+1

Find the derivative of the function. The ending result is our slope for the tangent line.

Using any of the rules necessary, derive the function.

Using the example f(x)=3x 3 -6, let us derive it.

First, we need to identify which rule(s) we should use. Since there is no expression multiplication or division, we do not need to use either the Product Rule or the Quotient Rule. Since there is no inner and outer function, we do not have to use the Chain Rule. We must use the Power Rule to derive the function. Let's break it up into pieces. The first piece is **3x 3 ** Using the Power Rule, the exponent of 3 multiplies with the constant 3 to give us a new constant of 9. When using the Power Rule, is is extremely important to remember to bump the exponent down one after multiplying it with the constant. In this case, the exponent of 3 drops down to an exponent of 2. Hence, our derivative of this specific piece is **9x 2 .** The next piece is **-6.** -6 is a constant. The Constant Rule states that the derivative of any constant is 0. Therefore, the derivative of -6 is 0. Since we have in essence, nothing after deriving this piece, we do not write out the 0.

Therefore, the entire derivative of f(x)=3x 3 -6 is 9x 2.

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