Help please

[Will1234]

Can someone please help me figure out the derivative of this function
If possible can you explain it and or show how you got it

 

[Deleted member 4993]

Can someone please help me figure out the derivative of this function
If possible can you explain it and or show how you got it

View attachment 33215

Hint: First use log() on both sides - then differentiate

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[Harry_the_cat]

Do you know how to differentiate \(\displaystyle y=2^x\)?

 

[Steven G]

Do you know how to differentiate y=2^-x?

 

[nasi112]

Let
\(\displaystyle y = f(x)\)

Now you have
\(\displaystyle y = 2^{4-x} + 12\)

Move 12 to the left
\(\displaystyle y - 12 = 2^{4-x}\)

Take the logarithm of both sides
\(\displaystyle \ln(y - 12) = (4 - x)\ln(2)\)

Hint: Use implicit differentiation to find \(\displaystyle \frac{dy}{dx}\).

 

[Deleted member 4993]

Further hint:

u = ln(x)

\(\displaystyle \frac{du}{dx} \ = \ \frac{1}{x}\)

 

[Steven G]

The above method is how I would solve such a problem because I do not remember the rule.
Sure you should be able to derive the rule or solve the problem as shown above.
I suspect that you are a calculus student and that both your instructor and textbook gave you the rule to differentiate f(x) = a^u, where a is a constant and u is a function of x.
[a^u]' = a^u*ln(a)*u'
Your a is 2 and your u is 4-x
So [2^4-x]' = 2^4-x*ln(2)*(??)

 

[Will1234]

Thank you for all your help this helped me a lot