- $ y = 10x^3 $ → $ \frac{dy}{dx} = 30x^2 $
- $ y = \frac{1}{2}x^{-2} $ → $ \frac{dy}{dx} = -x^{-3} $
- $ y = \frac{1}{2\sqrt{x}} = \frac{1}{2}x^{-1/2} $ → $ \frac{dy}{dx} = -\frac{1}{4}x^{-3/2} $
- $ y = 3x^{-1/15} $ → $ \frac{dy}{dx} = -\frac{1}{5}x^{-16/15} $
- $ y = 8x^6 + 2x^{17} $ → $ \frac{dy}{dx} = 48x^5 + 34x^{16} $
- $ y = \sqrt[5]{x} = x^{1/5} $ → $ \frac{dy}{dx} = \frac{1}{5}x^{-4/5} $
- $ y = x^{1/21} + x^{-1/7} $ → $ \frac{dy}{dx} = \frac{1}{21}x^{-20/21} - \frac{1}{7}x^{-8/7} $
- $ y = 2x^{12} + 6x^7 + x^4 $ → $ \frac{dy}{dx} = 24x^{11} + 42x^6 + 4x^3 $
- $ y = \frac{5}{3}x^3 - \frac{7}{6}x^6 + \frac{6}{4}x^8 $ → $ \frac{dy}{dx} = 5x^2 - 7x^5 + 12x^7 $
- $ y = \frac{1}{2}x^{3/2} - \frac{22}{7}x^{-5/2} + x^{3/7} $ → $ \frac{dy}{dx} = \frac{3}{4}x^{1/2} + \frac{55}{7}x^{-7/2} + \frac{3}{7}x^{-4/7} $
Parent Tip: Review the logic above to help your child master the concept of product rule for derivatives worksheet.
