Question

Find the derivative of the problem below and show your work.

Answer 1

The derivative of the function is =$\frac{e^x\left(4x^2-8x+1\right)}{2\left(4x^2+1\right)^2}$

What is Derivative?

The derivative is the instantaneous rate of change of a function with respect to one of its variables.

Given function:

y=$\left(\frac{e^x}{\:\left(8x^2+2\right)}\right)$

Differentiating and applying Quotient Rule

=$\frac{\frac{d}{dx}\left(e^x\right)\left(8x^2+2\right)-\frac{d}{dx}\left(8x^2+2\right)e^x}{\left(8x^2+2\right)^2}$

Now, d/dx ($e^{x}$)= ($e^{x}$)

d/dx(8x²+2) = 16x

So,

=$\frac{e^x\left(8x^2+2\right)-16xe^x}{\left(8x^2+2\right)^2}$

=$\frac{e^x\left(4x^2-8x+1\right)}{2\left(4x^2+1\right)^2}$

Hence, the value of derivative is  $\frac{e^x\left(4x^2-8x+1\right)}{2\left(4x^2+1\right)^2}$

Learn more about derivative here:

brainly.com/question/124529

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