y = 4x^{2}-\\frac{1}{x}\nthe derivative of\ny = 8x - x^{-2}\ny = x^{-2}+8x\ny = 2x - x^{-2}\ny = x^{-1}+8x
y = 4x^{2}-\\frac{1}{x}\nthe derivative of\ny = 8x - x^{-2}\ny = x^{-2}+8x\ny = 2x - x^{-2}\ny = x^{-1}+8x
Answer
Explanation:
Step1: Apply derivative rules
Use the power rule: ((x^n)^\prime = nx^{n - 1}). For (y = 4x^2-\frac{1}{x}=4x^2 - x^{-1}). The derivative of (4x^2) is (4\times2x^{2 - 1}=8x). The derivative of (-x^{-1}) is (-(-1)x^{-1 - 1}=x^{-2}).
Step2: Combine derivatives
(y^\prime=(4x^2 - x^{-1})^\prime=(4x^2)^\prime-(x^{-1})^\prime). So (y^\prime = 8x+x^{-2}).
Answer:
(y^\prime=x^{-2}+8x)