3.3: Homework- Power Rule

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Compute the following derivatives. Do not use the definition of the derivative. Instead, use the linearity and power rules we talked about in this section.
1. $\cfrac{d}{dx}\ x^{15}$
  $15 x^{14}$
  ans
2. $\cfrac{d}{dx}\ 3x^6$
  $18x^5$
  ans
3. $\cfrac{d}{dx}\ \cfrac{1}{2}x^{4}$
  $2x^3$
  ans
4. $\cfrac{d}{dx}\ 3 x^2 + 6x - 1$
  $6x + 6$
  ans
5. $\cfrac{d}{dx}\ (2x + 3)^2$
  $8x + 12$
  ans
6. $quicklatex.com-b7aa47f24778b43bcc1911cc98356c1b_l3.png$
  $quicklatex.com-2d27cd06f8036f258b4209825c9bc716_l3.png$
  ans
7. $\cfrac{d}{dx}\ 7 x^{-4}$
  $-28x^{-5}$
  ans
8. $quicklatex.com-e4fc234147db953ac68f81a626d6b117_l3.png$
  $quicklatex.com-ed18e5eb3d2e9bc4fdc204ca5f98769b_l3.png$
  ans
9. $\cfrac{d}{dx}\ \sqrt{x}$
  $quicklatex.com-8c55e4fecd36610200c4286410ee6a3f_l3.png$
  ans
10. $\cfrac{d}{dx}\ \frac{1}{x}$
  $-x^{-2}$
  ans
11. $\cfrac{d}{dx}\ \sqrt[3]{x^2}$
  $quicklatex.com-f20972d78f1298dea85dffe77636b027_l3.png$
  ans
12. $\cfrac{d}{dx}\ \frac{2}{\sqrt{x}}$
  $quicklatex.com-8ff315cd0ad85e8437433130af51e18d_l3.png$
  ans

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