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Find the derivative of $y=1 / x^{3}$ as (a) a quotient and (b) a negative power of $x$ and show that the results are the same.

$$\frac{x^{3}(0)-1\left(3 x^{2}\right)}{x^{6}}=-3 x^{-4}$$

Calculus 1 / AB

Chapter 23

The Derivative

Section 7

The Derivative of a Power of a Function

Derivatives

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to solve for the derivative of F of X is equal to X cubed times three to the X. We need to use the product rule, which is the derivative of the first times a second plus the derivative the second times first so we can set or two functions g of X, be X cubed and h of X to be three to the X. So we need to find what the derivative of G of x Q Prime X it's equal to, and that is the form three times X to the three minus one just to so three X squared. That's work h prime. We have an exponential function which is equal to the original function three to the X Times the natural log of the base three. So we can use this to put it all together. So through the 1st 3 x squared times a second three of the X waas derivative of the 2nd 3 to the X natural lock of free put that incorrect. This used to make it clear times first, pecs Cute that it's our derivatives should probably make that clear that prime X is equal to that x three x squared three to the ax plus three to the X natural log of three times execute

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