Simplifying derivatives. Need Help Please! Urgent!

[bolzcarz328]

I'm having trouble with the question:
Using the function: y=x/4^x show that the most simplified derivitave is y'= (1-2x*ln2)/4^x

 

[Deleted member 4993]

Start with:

\(\displaystyle \frac{d}{dx}(4^x)\) = ?

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Please share your work/thoughts about this assignment.

 

[pka]

I'm having trouble with the question: Using the function: y=x/4^x show that the most simplified derivative is y'= (1-2x*ln2)/4^x

From what you posted it is hard to know exactly where you are having trouble.
I will suggest writing this as \(\displaystyle D_x\left(x\cdot 4^{-x}\right)=\left(4^{-x}-4^{-x}\cdot\log(4)\cdot x\right)=\left(\dfrac{1-\log(4)\cdot x}{4^{x}}\right)\)
You can see that I use \(\displaystyle \log\) where you use \(\displaystyle \ln\) that is the trend in usage.
Can you finish?