Chapter 2 - Differentiation - 2.2 Exercises: 42

The derivative is $8-\frac{6}{x^3}$.

Work Step by Step

Rewrite the function as $y = 8x+3x^{-2}$. To find $y'$, differentiate the individual terms using the power rule $((x^n)' = nx^{n-1})$. The derivative of $8x$ is $8$. The derivative of $3x^{-2}$ is equal to $(3)(-2)(x^{-2-1})$ which simplifies to $-\frac{6}{x^3}$. By summing everything together, we get $y' = 8-\frac{6}{x^3}$.

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