Help please

Will1234

New member
Joined
Jun 23, 2022
Messages
2
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

1656031906096.png
 

Attachments

  • image.jpg
    image.jpg
    2.5 MB · Views: 4
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.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem

1656034665429.png
 
Last edited by a moderator:
Let
y=f(x)\displaystyle y = f(x)

Now you have
y=24x+12\displaystyle y = 2^{4-x} + 12

Move 12 to the left
y12=24x\displaystyle y - 12 = 2^{4-x}

Take the logarithm of both sides
ln(y12)=(4x)ln(2)\displaystyle \ln(y - 12) = (4 - x)\ln(2)

Hint: Use implicit differentiation to find dydx\displaystyle \frac{dy}{dx}.
 
Further hint:

u = ln(x)

dudx = 1x\displaystyle \frac{du}{dx} \ = \ \frac{1}{x}
 
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) = au, where a is a constant and u is a function of x.
[au]' = au*ln(a)*u'
Your a is 2 and your u is 4-x
So [24-x]' = 24-x*ln(2)*(??)
 
Top