Chapter 11, Problem 1RE

In Problems 1-12, find the derivative of each function.

$y=10e^{3x^2-x}$

To determine

To calculate: The derivative of the provided function $y=10e^{3x^2-x}$.

Answer to Problem 1RE

Solution:

The required derivative is $\underset{\_}{10e^{3x^2-x}\left(6x-1\right)}$.

Explanation of Solution

Given Information:

The provided function is:

$y=10e^{3x^2-x}$

Formula used:

The derivatives of exponential function:

$\frac{d}{dx}{e}^{f\left(x\right)}=e^{f\left(x\right)}\frac{d}{dx}f\left(x\right)$

Where $f\left(x\right)$ is a differentiable function of $x$.

Calculation:

Consider the provided function:

$y=10e^{3x^2-x}$

Differentiate both sides with respect to $x$ as:

$\frac{dy}{dx}=\frac{d}{dx}\left(10e^{3x^2-x}\right)$

Now, use the exponential rule of derivatives:

$\begin{array}{c}\frac{dy}{dx}=\frac{d}{dx}\left(10e^{3x^2-x}\right)\\ =10e^{3x^2-x}\frac{d\left(3x^2-x\right)}{dx}\\ =10e^{3x^2-x}\left\{\frac{d\left(3x^2\right)}{dx}-\frac{d\left(x\right)}{dx}\right\}\\ =10e^{\left(3x^2-x\right)}\left(6x-1\right)\end{array}$

Thus, the required derivative is $10e^{3x^2-x}\left(6x-1\right)$.