Chapter 14, Problem 64RE

To determine

To find:

The differentiation of the given function

Answer to Problem 64RE

Differentiating the function is $y^{\prime }\left(x\right)=\frac{dy}{dx}=4x+4$

Explanation of Solution

Given:

The function is

  $f\left(x\right)=2x^2+4x$

Concept used:

Definition of the differentiation:-Differentiation is the action of computing a derivative

The derivative of a function $y=f\left(x\right)$ of a variable $x$ is a measure of the rate at which the value y of the function changes with respect to $x$

Calculation:

The function

  $f\left(x\right)=2x^2+4x\mathrm{...................}\left(1\right)$

The derivative of a function

  $\begin{array}{l}y=f\left(x\right)\\ y^{\prime }=f^{\prime }\left(x\right)=\frac{dy}{dx}\end{array}$

Differentiating the equation (1) with respect to $x$

  $\begin{array}{l}\frac{dy}{dx}=\frac{d}{dx}\left(2x^2+4x\right)\\ \frac{dy}{dx}=4x+\mathrm{4...............}\left(2\right)\end{array}$

Putting $x=3$ in equation (2)

  $\begin{array}{l}{y}^{\prime }\left(x\right)=\frac{dy}{dx}=4x+4\\ y^{\prime }\left(-1\right)=4\left(-1\right)+4\\ y^{\prime }\left(-1\right)=-4+4\\ y^{\prime }\left(-1\right)=0\end{array}$