The derivative of the function is =![\frac{e^x\left(4x^2-8x+1\right)}{2\left(4x^2+1\right)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5Ex%5Cleft%284x%5E2-8x%2B1%5Cright%29%7D%7B2%5Cleft%284x%5E2%2B1%5Cright%29%5E2%7D)
<h3>What is Derivative?</h3>
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)](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7Be%5Ex%7D%7B%5C%3A%5Cleft%288x%5E2%2B2%5Cright%29%7D%5Cright%29)
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}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28e%5Ex%5Cright%29%5Cleft%288x%5E2%2B2%5Cright%29-%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%288x%5E2%2B2%5Cright%29e%5Ex%7D%7B%5Cleft%288x%5E2%2B2%5Cright%29%5E2%7D)
Now, d/dx (
)= (
)
d/dx(8x²+2) = 16x
So,
=![\frac{e^x\left(8x^2+2\right)-16xe^x}{\left(8x^2+2\right)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5Ex%5Cleft%288x%5E2%2B2%5Cright%29-16xe%5Ex%7D%7B%5Cleft%288x%5E2%2B2%5Cright%29%5E2%7D)
=![\frac{e^x\left(4x^2-8x+1\right)}{2\left(4x^2+1\right)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5Ex%5Cleft%284x%5E2-8x%2B1%5Cright%29%7D%7B2%5Cleft%284x%5E2%2B1%5Cright%29%5E2%7D)
Hence, the value of derivative is ![\frac{e^x\left(4x^2-8x+1\right)}{2\left(4x^2+1\right)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5Ex%5Cleft%284x%5E2-8x%2B1%5Cright%29%7D%7B2%5Cleft%284x%5E2%2B1%5Cright%29%5E2%7D)
Learn more about derivative here:
brainly.com/question/124529
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Answer:
h=12.5
Step-by-step explanation:
It’s a right triangle, so you can use the Pythagorean Theorem.
9.2²+8.5²=h²
84.64+72.25=h²
156.89=h²
√156.89=h
h=12.5255
h=12.5
Answer:
1. x = 7
Step-by-step explanation:
12x + 16 = 100
12x = 84
x = 7