- 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.
- [latex]\cfrac{d}{dx}\ x^{15}[/latex]
[latex]15 x^{14}[/latex]ans
- [latex]\cfrac{d}{dx}\ 3x^6[/latex]
[latex]18x^5[/latex]ans
- [latex]\cfrac{d}{dx}\ \cfrac{1}{2}x^{4}[/latex]
[latex]2x^3[/latex]ans
- [latex]\cfrac{d}{dx}\ 3 x^2 + 6x - 1[/latex]
[latex]6x + 6[/latex]ans
- [latex]\cfrac{d}{dx}\ (2x + 3)^2[/latex]
[latex]8x + 12[/latex]ans
- [latex]\cfrac{d}{dx}\ x^{1/3}[/latex]
[latex]\frac{1}{3} x^{-2/3}[/latex]ans
- [latex]\cfrac{d}{dx}\ 7 x^{-4}[/latex]
[latex]-28x^{-5}[/latex]ans
- [latex]\cfrac{d}{dx}\ 2x^{-1/2} + 4x^{1/2}[/latex]
[latex]-x^{-3/2} + 2x^{-1/2}[/latex]ans
- [latex]\cfrac{d}{dx}\ \sqrt{x}[/latex]
[latex]\frac{1}{2}x^{-1/2}[/latex]ans
- [latex]\cfrac{d}{dx}\ \frac{1}{x}[/latex]
[latex]-x^{-2}[/latex]ans
- [latex]\cfrac{d}{dx}\ \sqrt[3]{x^2}[/latex]
[latex]\frac{2}{3} x^{-1/3}[/latex]ans
- [latex]\cfrac{d}{dx}\ \frac{2}{\sqrt{x}}[/latex]
[latex]-x^{-3/2}[/latex]ans
- [latex]\cfrac{d}{dx}\ x^{15}[/latex]