Find the derivative of the function by using the Product Rule. Simplify your answer. f(x) = (x - 3)(x + 3)
2 answers:
Answer:
![f'(x)=2x](https://tex.z-dn.net/?f=f%27%28x%29%3D2x)
Step-by-step explanation:
To Find :Find the derivative of the function by using the Product Rule. Simplify your answer. f(x) = (x - 3)(x + 3)
Solution :
![f(x) = (x - 3)(x + 3)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20-%203%29%28x%20%2B%203%29)
We will use chain rule of product
Formula : ![uv=u \times v' +v \tyimes u'](https://tex.z-dn.net/?f=uv%3Du%20%5Ctimes%20v%27%20%2Bv%20%5Ctyimes%20u%27)
=![(x-3) \times 1+(x+3) \times 1](https://tex.z-dn.net/?f=%28x-3%29%20%5Ctimes%201%2B%28x%2B3%29%20%5Ctimes%201)
=![(x-3)+(x+3)](https://tex.z-dn.net/?f=%28x-3%29%2B%28x%2B3%29%20)
=![2x](https://tex.z-dn.net/?f=2x)
So, ![f'(x)=2x](https://tex.z-dn.net/?f=f%27%28x%29%3D2x)
Hence the derivative of the function by using the Product Rule is 2x
Answer:
![f'(x)=2x](https://tex.z-dn.net/?f=f%27%28x%29%3D2x)
Step-by-step explanation:
Given : Function ![f(x)=(x-3)(x+3)](https://tex.z-dn.net/?f=f%28x%29%3D%28x-3%29%28x%2B3%29)
To find : The derivative of the function by using the Product Rule ?
Solution :
The product rule of derivative is
![\frac{d}{dx}(u\cdot v)=uv'+vu'](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28u%5Ccdot%20v%29%3Duv%27%2Bvu%27)
Here, u=x-3 and v=x+3
![\frac{d}{dx}((x-3)\cdot (x+3))=(x-3)\frac{d}{dx}(x+3)+(x+3)\frac{d}{dx}(x-3)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%28x-3%29%5Ccdot%20%28x%2B3%29%29%3D%28x-3%29%5Cfrac%7Bd%7D%7Bdx%7D%28x%2B3%29%2B%28x%2B3%29%5Cfrac%7Bd%7D%7Bdx%7D%28x-3%29)
![\frac{d}{dx}((x-3)\cdot (x+3))=(x-3)1+(x+3)1](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%28x-3%29%5Ccdot%20%28x%2B3%29%29%3D%28x-3%291%2B%28x%2B3%291)
![\frac{d}{dx}((x-3)\cdot (x+3))=x-3+x+3](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%28x-3%29%5Ccdot%20%28x%2B3%29%29%3Dx-3%2Bx%2B3)
![\frac{d}{dx}((x-3)\cdot (x+3))=2x](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%28x-3%29%5Ccdot%20%28x%2B3%29%29%3D2x)
Therefore, ![f'(x)=2x](https://tex.z-dn.net/?f=f%27%28x%29%3D2x)
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