3.3: Homework- Power Rule
- Page ID
- 88643
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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.
- \(\cfrac{d}{dx}\ x^{15}\)
\(15 x^{14}\)ans
- \(\cfrac{d}{dx}\ 3x^6\)
\(18x^5\)ans
- \(\cfrac{d}{dx}\ \cfrac{1}{2}x^{4}\)
\(2x^3\)ans
- \(\cfrac{d}{dx}\ 3 x^2 + 6x - 1\)
\(6x + 6\)ans
- \(\cfrac{d}{dx}\ (2x + 3)^2\)
\(8x + 12\)ans
ans- \(\cfrac{d}{dx}\ 7 x^{-4}\)
\(-28x^{-5}\)ans
ans- \(\cfrac{d}{dx}\ \sqrt{x}\)
ans - \(\cfrac{d}{dx}\ \frac{1}{x}\)
\(-x^{-2}\)ans
- \(\cfrac{d}{dx}\ \sqrt[3]{x^2}\)
ans - \(\cfrac{d}{dx}\ \frac{2}{\sqrt{x}}\)
ans
- \(\cfrac{d}{dx}\ x^{15}\)