Chapter 11, Problem 69RE

To determine

To Find: The derivative of $g(x)=4x^2-x$

Answer to Problem 69RE

  $g\text{'}(x)=8x-1$

Explanation of Solution

Given information:

  $g(x)=4x^2-x$

Concept and Formula Used:

  $\frac{d}{dx}a=0\text{ where 'a' is constant,}\frac{d}{dx}{x}^n=n{x}^{n-1}$

Calculation:

The given function is $g(x)=4x^2-x$

Differentiate both sides with respect to ‘x’

  $\begin{array}{l}\frac{d}{dx}g(x)=\frac{d}{dx}\left(4x^2-x\right)\\ g\text{'}(x)=4\frac{d}{dx}{x}^2-\frac{dx}{dx}\\ \frac{d}{dx}{x}^n=n{x}^{n-1}\\ g\text{'}(x)=4\left(2x^{2-1}\right)-1\\ g\text{'}(x)=8x-1\end{array}$

Conclusion:

  $g\text{'}(x)=8x-1$